This paper investigates the diffusive predator-prey system with nonmonotonic functional response and fear effect. Firstly, we discussed the stability of the equilibrium solution for a corresponding ODE system. Secondly, we established a priori positive upper and lower bounds for the positive solutions of the PDE system. Thirdly, sufficient conditions for the local asymptotical stability of two positive equilibrium solutions of the system are given by using the method of eigenvalue spectrum analysis of linearization operator. (...) Finally, the existence and nonexistence of nonconstant positive steady states of this reaction-diffusion system are established by the Leray–Schauder degree theory and Poincaré inequality. (shrink)

Theoretical and experimental studies on prey–predator systems where predator is supplied with alternate sources of food have received significant attention over the years due to their relevance in achieving biological conservation and biological control. Some of the outcomes of these studies suggest that with appropriate quality and quantity of additional food, the system can be steered towards any desired state eventually with time. One of the limitations of previous studies is that the desired state is reached (...) asymptotically, which makes the outcomes not easily applicable in practical scenarios. To overcome this limitation, in this work, we formulate and study optimal control problems to achieve the desired outcomes in minimum (finite) time. We consider two different models of additional food provided prey–predator systems involving Holling type IV functional response (with inhibitory effect of prey). In the first scenario, additional food is incorporated implicitly into the predator’s functional response with a possibility of achieving biological conservation through co-existence of species and biological control by maintaining prey at a level that is least harmful to the system. In the second, the effect of additional food is incorporated explicitly into the predator’s compartment with the goal of pest management by maintaining prey density at a very minimal damaging level. For both cases, appropriate optimal control strategies are derived and the theoretical findings are illustrated by numerical simulations. We also discuss the ecological significance of the theoretical findings for both models. (shrink)

This paper establishes a model on the upstream and downstream relationship among private enterprises, provincial and local officials, and the central government in the real estate market using the population ecology theory of mutual relations among individual species from the perspective of business ecosystem. A dynamic model is introduced and the complex dynamical behaviors of such a predator-prey model are investigated by means of numerical simulation. The local stability conditions and complex dynamics are investigated, and the existence of (...) chaos is discussed in the sense of Marotto theorem; bifurcation diagrams, Lyapunov exponents, sensitivity analysis for initial values, and time history figure of the system are mapped out and discussed. This shows that there are two routes to complicated dynamics, one of which is the cascade of flip bifurcations resulting in periodic cycles, and the other one is Neimark-Sacker bifurcation which produces attractive invariant closed curves. We arrive at conclusions that the phenomenon of chaos is harmful to private enterprises, and unstable behavior is often unfavorable. Thus, linear feedback control is applied to drive the model to a stable state when the system exhibits chaotic behaviors, achieving the goal of eliminating the negative effects to a large extent. (shrink)

This paper deals with designing a harvesting control strategy for a predator–prey dynamical system, with parametric uncertainties and exogenous disturbances. A feedback control law for the harvesting rate of the predator is formulated such that the population dynamics is asymptotically stabilized at a positive operating point, while maintaining a positive, steady state harvesting rate. The hierarchical block strict feedback structure of the dynamics is exploited in designing a backstepping control law, based on Lyapunov theory. In order (...) to account for unknown parameters, an adaptive control strategy has been proposed in which the control law depends on an adaptive variable which tracks the unknown parameter. Further, a switching component has been incorporated to robustify the control performance against bounded disturbances. Proofs have been provided to show that the proposed adaptive control strategy ensures asymptotic stability of the dynamics at a desired operating point, as well as exact parameter learning in the disturbance-free case and learning with bounded error in the disturbance prone case. The dynamics, with uncertainty in the death rate of the predator, subjected to a bounded disturbance has been simulated with the proposed control strategy. (shrink)

In this work, our aim is to investigate the impact of a non-Kolmogorov predator-prey-subsidy model incorporating nonlinear prey refuge and the effect of fear with Holling type II functional response. The model arises from the study of a biological system involving arctic foxes, lemmings, and seal carcasses. The positivity and asymptotically uniform boundedness of the solutions of the system have been derived. Analytically, we have studied the criteria for the feasibility and stability of different equilibrium (...) points. In addition, we have derived sufficient conditions for the existence of local bifurcations of codimension 1. It is also observed that there is some time lag between the time of perceiving predator signals through vocal cues and the reduction of prey’s birth rate. So, we have analyzed the dynamical behaviour of the delayed predator-prey-subsidy model. Numerical computations have been performed using MATLAB to validate all the analytical findings. Numerically, it has been observed that the predator, prey, and subsidy can always exist at a nonzero subsidy input rate. But, at a high subsidy input rate, the prey population cannot persist and the predator population has a huge growth due to the availability of food sources. (shrink)

Spatial predator-prey models have been studied by researchers for many years, because the exact distributions of the population can be well illustrated via pattern formation. In this paper, amplitude equations of a spatial Holling–Tanner predator-prey model are studied via multiple scale analysis. First, by amplitude equations, we obtain the corresponding intervals in which different kinds of patterns will be onset. Additionally, we get the conclusion that pattern transitions of the predator are induced by the increasing (...) rate of conversion into predator biomass. Specifically, pattern transitions of the predator between distinct Turing pattern structures vary in an orderly manner: from spotted patterns to stripe patterns, and finally to black-eye patterns. Moreover, it is discovered that pattern transitions of prey can be induced by cross-diffusion; that is, patterns of prey transmit from spotted patterns to stripe patterns and finally to a mixture of spot and stripe patterns. Meanwhile, it is found that both effects of cross-diffusion and interaction between the prey and predator can lead to the complicated phenomenon of dynamics in the system of biology. (shrink)

One of the most efficient predator-prey models with spatial effects is the one with ratio-dependent functional response. However, there is a need to further explore the effects of spatial motion on the dynamic behavior of population. In this work, we study a ratio-dependent predator-prey model with diffusion terms. The aim of this work is to investigate the changes in predator’s distribution in space as the prey populations change their mobility. We observe that the frequency (...) diffusion of the prey gives rise to the sparse density of the predator. Moreover, we also observe that the increasing rate of the conversion into predator biomass induces pattern transitions of the predator. Specifically speaking, Turing pattern of the predator populations goes gradually from a spotted pattern to a black-eye pattern, with the intermediate state being the mixture of spot and stripe pattern. The simulation results and analysis of this work illustrate that the diffusion rate and the real intrinsic factor influence the persistence of the predator-prey system mutually. (shrink)

This paper presents the intelligent virtual animals that inhabit Omosa, a virtual learning environment to help secondary school students learn how to conduct scientific inquiry and gain concepts from biology. Omosa supports multiple agents, including animals, plants, and human hunters, which live in groups of varying sizes and in a predator-prey relationship with other agent types (species). In this paper we present our generic agent architecture and the algorithms that drive all animals. We concentrate on two of our (...) animals to present how different parameter values affect their movements and inter/intra-group interactions. Two evaluations studies are included: one to demonstrate the effect of different components of our architecture; another to provide domain expert validation of the animal behavior. (shrink)

In this paper, we propose a time-delayed predator-prey model with Holling-type II functional response, which incorporates the gestation period and the cost of fear into prey reproduction. The dynamical behavior of this system is both analytically and numerically investigated from the viewpoint of stability, permanence, and bifurcation. We found that there are stability switches, and Hopf bifurcations occur when the delay τ passes through a sequence of critical values. The explicit formulae which determine the direction, stability, (...) and other properties of the bifurcating periodic solutions are given by using the normal form theory and center manifold theorem. We perform extensive numerical simulations to explore the impact of some important parameters on the dynamics of the system. Numerical simulations show that high levels of fear have a stabilizing effect while relatively low levels of fear have a destabilizing effect on the predator-prey interactions which lead to limit-cycle oscillations. We also found that the model with or without a delay-dependent factor can have a significantly different dynamics. Thus, ignoring the delay or not including the delay-dependent factor might result in inaccurate modelling predictions. (shrink)

In presence of predator population, the prey population may significantly change their behavior. Fear for predator population enhances the survival probability of prey population, and it can greatly reduce the reproduction of prey population. In this study, we propose a predator-prey fishery model introducing the cost of fear into prey reproduction with Holling type-II functional response and prey-dependent harvesting and investigate the global dynamics of the proposed model. For the system (...) without harvest, it is shown that the level of fear may alter the stability of the positive equilibrium, and an expression of fear critical level is characterized. For the harvest system, the existence of the semitrivial order-1 periodic solution and positive order- q periodic solution is discussed by the construction of a Poincaré map on the phase set, and the threshold conditions are given, which can not only transform state-dependent harvesting into a cycle one but also provide a possibility to determine the harvest frequency. In addition, to ensure a certain robustness of the adopted harvest policy, the threshold condition for the stability of the order- q periodic solution is given. Meanwhile, to achieve a good economic profit, an optimization problem is formulated and the optimum harvest level is obtained. Mathematical findings have been validated in numerical simulation by MATLAB. Different effects of different harvest levels and different fear levels have been demonstrated by depicting figures in numerical simulation using MATLAB. (shrink)

The main concern of this paper is to study the dynamic of a predator–prey system with diffusion. It incorporates the Holling-type-II and a modified Leslie–Gower functional responses under Robin boundary conditions. More concretely, we study the dissipativeness of the system by using the comparison principle, and we derive a criteria for permanence and for predator extinction.

We describe a prey–predator system incorporating constant prey refuge through provision of alternative food to predators. The proposed model deals with a problem of non-selective harvesting of a prey–predator system in which both the prey and the predator species obey logistic law of growth. The long-run sustainability of an exploited system is discussed through provision of alternative food to predators. We have analyzed the variability of the system in presence (...) of constant prey refuge and examined the stabilizing effect on predator–prey system. The steady states of the system are derived and dynamical behavior of the system is extensively analyzed around steady states. The optimal harvesting policy is formulated and solved with the help of Pontryagin’s maximal principle. Our objective is to maximize the monetary social benefit through protecting the predator species from extinction, keeping the ecological balance. Results finally illustrated with the help of numerical examples. (shrink)

A diffusive predator-prey system with both the additive Allee effect and the fear effect in the prey subject to Neumann boundary conditions is considered in this paper. Firstly, non-negative and non-trivial solution a priori estimations are shown. Furthermore, for specific parameter ranges, the absence of non-constant positive solutions is demonstrated. Secondly, we use the linearized theory to investigate the stability of non-negative constant solutions. The spatially homogeneous and non-homogeneous periodic solutions, as well as non-constant steady state (...) solutions, are next investigated by using Allee effect parameters as the bifurcation parameter. Finally, numerical simulation is used to illustrate some theoretical results. (shrink)

We propose a mathematical model for a class of predator–prey systems more complex than the usual one, involving a commensalism effect consisting in an influence of the predator on the sustainability of the prey. This effect induces interesting new features, including bi-stability. The question of the possibility of reaching a certain attractor starting from initial conditions with a small population of predators, which presents an interest from the vewpoint of the onset of the predator in (...) evolution, is addressed. We propose two possibilities: the classical one involving adapted conditions in the far past and a new one using biodiversity, specifically the presence of another predator which operates as a starter, being displaced in the sequel. (shrink)

Quantum frameworks for modeling competitive ecological systems and self-organizing structures have been investigated under multiple perspectives yielded by quantum mechanics. These comprise the description of the phase-space prey–predator competition dynamics in the framework of the Weyl–Wigner quantum mechanics. In this case, from the classical dynamics described by the Lotka–Volterra (LV) Hamiltonian, quantum states convoluted by statistical gaussian ensembles can be analytically evaluated. Quantum modifications on the patterns of equilibrium and stability of the prey–predator dynamics can then (...) be identified. These include quantum distortions over the equilibrium point drivers of the LV dynamics which are quantified through the Wigner current fluxes obtained from an onset Hamiltonian background. In addition, for gaussian ensembles highly localized around the equilibrium point, stability properties are shown to be affected by emergent topological quantum domains which, in some cases, could lead either to extinction and revival scenarios or to the perpetual coexistence of both prey and predator agents identified as quantum observables in microscopic systems. Conclusively, quantum and gaussian statistical driving parameters are shown to affect the stability criteria and the time evolution pattern for such microbiological-like communities. (shrink)

A stochastic prey-predator system in a polluted environment with Beddington-DeAngelis functional response is proposed and analyzed. Firstly, for the system with white noise perturbation, by analyzing the limit system, the existence of boundary periodic solutions and positive periodic solutions is proved and the sufficient conditions for the existence of boundary periodic solutions and positive periodic solutions are derived. And then for the stochastic system, by introducing Markov regime switching, the sufficient conditions for extinction or (...) persistence of such system are obtained. Furthermore, we proved that the system is ergodic and has a stationary distribution when the concentration of toxicant is a positive constant. Finally, two examples with numerical simulations are carried out in order to illustrate the theoretical results. (shrink)

Provision of additional food supplements for the purpose of biological conservation has been widely researched both theoretically and experimentally. The study of these biosystems is usually done using predator–prey models. In this paper, we consider an additional food provided predator–prey system in the presence of the inhibitory effect of the prey. This model is analyzed in the control parameter space using the control parameters, quality and quantity of additional food. The findings suggest that with (...) appropriate choice of additional food to predators, the biosystem can be controlled and steered to a desirable state. It is also possible to eliminate either of the interacting species. The vital role of the quality and quantity of the additional food in the system dynamics cautions the eco manager on the choice of the additional food for realizing the goal in the biological conservation programme. (shrink)

The discrete-time system has more complex and chaotic dynamical behaviors as compared to the continuous-time system. This paper extends a discrete Leslie–Gower predator-prey system with the Allee effect in the predator’s population, whose dynamics are analyzed and explored. We have determined the equilibrium points and studied their local stability properties. We find that the system undergoes flip bifurcation and Neimark–Sacker bifurcation around the interior equilibrium point by choosing the Allee parameter as a bifurcation (...) parameter. We discuss the stability and direction of both bifurcations with the help of the normal form theory and center manifold theorem. The flip bifurcation and Neimark–Sacker bifurcation are the most common routes to the chaotic orbit in the discrete system. Moreover, we utilize state feedback, pole placement, and hybrid control methods to control the chaos in the system. The work is complete with the numerical simulations to confirm the analytical findings. (shrink)

Abstract“Sign stimuli” elicit specific patterns of behavior when an organism's motivation is appropriate. In the toad, visually released prey-catching involves orienting toward the prey, approaching, fixating, and snapping. For these action patterns to be selected and released, the prey must be recognized and localized in space. Toads discriminate prey from nonprey by certain spatiotemporal stimulus features. The stimulus-response relations are mediated by innate releasing mechanisms (RMs) with recognition properties partly modifiable by experience. Striato-pretecto-tectal connectivity determines the (...) RM's recognition and localization properties, whereas medialpallio-thalamo-tectal circuitry makes the system sensitive to changes in internal state and to prior history of exposure to stimuli. RMs encode the diverse stimulus conditions referring to the same prey object through different combinations of “specialized” tectal neurons, involving cells selectively tuned to prey features. The prey-selective neurons express the outcome of information processing in functional units consisting of interconnected cells. Excitatory and inhibitory interactions among feature-sensitive tectal and pretectal neurons specify the perceptual operations involved in distinguishing the prey from its background, selecting its features, and discriminating it from predators. Other connections indicate stimulus location. The results of these analyses are transmitted by specialized neurons projecting from the tectum to bulbar/spinal motor systems, providing a sensorimotor interface. Specific combinations of such projective neurons – mediating feature- and space-related messages – form “command releasing systems” that activate corresponding motor pattern generators for appropriate prey-catching action patterns. (shrink)

The Lotka–Volterra predator-prey-model is a widely known example of model-based science. Here we reexamine Vito Volterra’s and Umberto D’Ancona’s original publications on the model, and in particular their methodological reflections. On this basis we develop several ideas pertaining to the philosophical debate on the scientific practice of modeling. First, we show that Volterra and D’Ancona chose modeling because the problem in hand could not be approached by more direct methods such as causal inference. This suggests a philosophically insightful (...) motivation for choosing the strategy of modeling. Second, we show that the development of the model follows a trajectory from a “how possibly” to a “how actually” model. We discuss how and to what extent Volterra and D’Ancona were able to advance their model along that trajectory. It turns out they were unable to establish that their model was fully applicable to any system. Third, we consider another instance of model-based science: Darwin’s model of the origin and distribution of coral atolls in the Pacific Ocean. Darwin argued more successfully that his model faithfully represents the causal structure of the target system, and hence that it is a “how actually” model. (shrink)

This paper compares the heuristic potential of three metaphorical paired concepts used in the relevant literature to characterise global relationships between the anthroposphere and the ecosphere. Methodologically, the guiding question is whether and to what extent metaphorical theses can support an arrival at hypotheses which accurately reflect reality and possess explanatory force. The predator-prey model implies that the populations of two species in such a relationship in principle exhibit coupled oscillations, giving prey populations the possibility of periodic (...) regeneration. For some time, however, the most important indicators of human destruction of nature have been showing a relentless upward trend which appears to render the tumour-host metaphor more appropriate. Another fact which favours this analogy is that a tumour develops within its host and from its host's normal cells, in a similar way to the emergence of the anthroposphere from within the biosphere. But the parasite-host analogy also allows the formulation of fruitful hypotheses, since ecological parasitology is equally familiar with varieties of autoaggressive interaction and provides a means of focusing particularly on the adelphoparasitic hierarchy within the anthroposphere. (shrink)

Theorizing in ecology and evolution often proceeds via the construction of multiple idealized models. To determine whether a theoretical result actually depends on core features of the models and is not an artifact of simplifying assumptions, theorists have developed the technique of robustness analysis, the examination of multiple models looking for common predictions. A striking example of robustness analysis in ecology is the discovery of the Volterra Principle, which describes the effect of general biocides in predator-prey systems. This (...) paper details the discovery of the Volterra Principle and the demonstration of its robustness. It considers the classical ecology literature on robustness and introduces two individual-based models of predation, which are used to further analyze the Volterra Principle. The paper also introduces a distinction between parameter robustness, structural robustness, and representational robustness, and demonstrates that the Volterra Principle exhibits all three kinds of robustness. *Received September 2006; revised May 2007. ‡Earlier versions of this paper were presented at the Australasian Association of Philosophy, the London School of Economics, and the University of Bristol. The authors wish to thank those audiences as well as Patrick Forber, Ken Waters, Deena Skolnick Weisberg, Uri Wilensky, and Bill Wimsatt for many helpful comments. Special thanks to Giacomo Sillari for his assistance in translating Volterra's original paper and his insightful thoughts about Volterra's aims and methods. Some of the research in this paper was supported by NSF grant SES-0620887 to MW. †To contact the authors, please write to: Michael Weisberg, Department of Philosophy, University of Pennsylvania, 433 Logan Hall, Philadelphia, PA 19104; e-mail: [email protected]; Kenneth Reisman, Pluribo, Inc., 100 Park Avenue, Suite 1600, New York, NY 10017; e-mail: [email protected]. (shrink)

In this paper, we propose a new predator-prey nonlinear dynamic evolutionary model of real estate enterprises considering the large, medium, and small real estate enterprises for three different prey teams. A 5D predator-prey nonlinear dynamic evolutionary system in the real estate market is established, where the large, medium, and small real estate enterprises correspond to three differential equations, provincial and local officials, and the central government correspond to the other two differential equations. Nonlinear dynamic (...) analysis on a 5D predator-prey evolutionary system in the real estate market, containing the analysis of equilibrium points and stabilities, is made. The corresponding discrete system is simulated, and the simulation results about Lyapunov spectrum, bifurcation diagram, sequence diagram, and phase diagram are given. Compared with the work of Yang et al. in which all real estate enterprises corresponded to one differential equation, in our proposed model, the large, medium, and small real estate enterprises correspond to three differential equations which is more accordant with the specific circumstance of real estate companies. (shrink)

Predation and escaping from predation through hiding are two fundamental phenomena in ecology. The most common approach to reducing the chance of predation is to use a refuge. Here, we consider a three species fishery model system with prey refuge induced by a Holling type-II functional response. These three species of fish populations are named prey, middle predator, and top predator. Harvesting is employed in most fishery models to achieve both ecological and commercial benefits. Research (...) proves that non-linear harvesting (Michaelis–Menten type) returns more realistic outcomes. So, we have combined the Michaelis–Menten type of harvesting efforts for all populations. Uniform boundedness conditions for the solutions of the model are discussed. The existence conditions for possible equilibrium points with stability are presented. We explain the dynamical behavior at each equilibrium point through bifurcation analysis. The persistent criteria of the system are examined. Bionomic equilibrium and optimal harvesting control using Pontryagin’s maximum principle are calculated. For validation of the model in the real world, we have implemented this in the freshwater ecosystem of Lake Victoria. Extraction of native fish species and ecological balances are the foremost solicitude of Lake Victoria. We may resolve this concern partially by implementing prey refuge, since it may sustain the ecology of Lake Victoria, and therefore also its economical importance. Lake Victoria is acclaimed worldwide for the trade of fishing. Also, it provides the largest employment in east-central Africa and is beneficial to fishing equipment manufacturers. So, the bionomic equilibrium and harvesting control have significant applications in the fisheries. All the analytical studies are verified by numerical simulations. We have plotted phase portraits, bifurcation diagrams, Lyapunov exponents to explore the dynamics of the proposed model. (shrink)

Scientific models are important, if not the sole, units of science. This thesis addresses the following question: in virtue of what do scientific models represent their target systems? In Part i I motivate the question, and lay out some important desiderata that any successful answer must meet. This provides a novel conceptual framework in which to think about the question of scientific representation. I then argue against Callender and Cohen’s attempt to diffuse the question. In Part ii I investigate the (...) ideas that scientific models are ‘similar’, or structurally morphic, to their target systems. I argue that these approaches are misguided, and that at best these relationships concern the accuracy of a pre-existing representational relationship. I also pay particular attention to the sense in which target systems can be appropriately taken to exhibit a ‘structure’, and van Fraassen’s recent argument concerning the pragmatic equivalence between representing phenomena and data. My next target is the idea that models should not be seen as objects in their own right, but rather what look like descriptions of them are actually direct descriptions of target systems, albeit not ones that should be understood literally. I argue that these approaches fail to do justice to the practice of scientific modelling. Finally I turn to the idea that how models represent is grounded, in some sense, in their inferential capacity. I compare this approach to anti-representationalism in the philosophy of language and argue that analogous issues arise in the context of scientific representation. Part iii contains my positive proposal. I provide an account of scientific representation based on Goodman and Elgin’s notion of representation-as. The result is a highly conventional account which is the appropriate level of generality to capture all of its instances, whilst remaining informative about the notion. I illustrate it with reference to the Phillips-Newlyn machine, models of proteins, and the Lotka-Volterra model of predator-prey systems. These examples demonstrate how the account must be understood, and how it sheds light on our understanding of how models are used. I finally demonstrate how the account meets the desiderata laid out at the beginning of the thesis, and outline its implications for further questions from the philosophy of science; not limited to issues surrounding the applicability of mathematics, idealisation, and what it takes for a model to be ‘true’. (shrink)

A double delayed hybrid stochastic prey-predator bioeconomic system with Lévy jumps is established and analyzed, where commercial harvesting on prey and environmental stochasticity on population dynamics are considered. Two discrete time delays are utilized to represent the maturation delay of prey and gestation delay of predator, respectively. For a deterministic system, positivity of solutions and uniform persistence of system are discussed. Some sufficient conditions associated with double time delays are derived to discuss (...) asymptotic stability of interior equilibrium. For a stochastic system, existence and uniqueness of a global positive solution are studied. By using the invariant measure theory and singular boundary theory of diffusion process, existence of stochastic Hopf bifurcation and stochastic stability are investigated. By constructing appropriate Lyapunov functions, asymptotic dynamic behavior of the proposed hybrid stochastic system with double time delays and Lévy jumps is discussed. Numerical simulations are provided to show consistency with theoretical analysis. (shrink)

Models occupy a central role in the scientific endeavour. Among the many purposes they serve, representation is of great importance. Many models are representations of something else; they stand for, depict, or imitate a selected part of the external world (often referred to as target system, parent system, original, or prototype). Well-known examples include the model of the solar system, the billiard ball model of a gas, the Bohr model of the atom, the Gaussian-chain model of a (...) polymer, the MIT bag model of quark confinement, the Lorenz model of the atmosphere, the Lotka-Volterra model of the predator-prey interaction, or the hydraulic model of an economy, to mention just a few. All these models represent their target systems (or selected parts of them) in one way or another. (shrink)

On the basis of the previous publications, a new fractional-order prey-predator model is set up. Firstly, we discuss the existence, uniqueness, and nonnegativity for the involved fractional-order prey-predator model. Secondly, by analyzing the characteristic equation of the considered fractional-order Lotka–Volterra model and regarding the delay as bifurcation variable, we set up a new sufficient criterion to guarantee the stability behavior and the appearance of Hopf bifurcation for the addressed fractional-order Lotka–Volterra system. Thirdly, we perform the (...) computer simulations with Matlab software to substantiate the rationalisation of the analysis conclusions. The obtained results play an important role in maintaining the balance of population in natural world. (shrink)

The aim of this work is to present aggregation methods of hierarchically organized systems allowing one to replace the initial micro-system by a macro-system described by a few global variables. We also study the relations between the fast micro-dynamics and the slow macro-dynamics which can produce global properties. Emergence corresponds to a bottom-up coupling that is the result effected by a micro-level at a macro-level. As an example, we present prey-predator models with different time scales in (...) an heterogeneous environment. A fast time scale is associated to the migration process on spatial patches and a slow time scale is associated to growth and interactions between the populations. Preys must go on spatial patches where resources are located and where predators can attack them. The efficiency of the predators to catch preys is patch dependent. Perturbation methods allow us to aggregate the initial system of differential equations for the patch sub-populations into a macro-system of two differential equations governing the total population densities. We study the case of density independent and density dependent migrations. In the latter case, we show that different functional responses can emerge in the macro prey-predator model as a result of the coupling between the slow and fast systems. (shrink)

A standard platitude about the function of causal knowledge or theories is that they are valuable because they support prediction, explanation, and control. Knowledge of predator-prey relations enables us to predict future animal populations, as well as design policies or interventions that help influence those populations. If we understand the underlying biochemical mechanisms of some disease, then we can predict who is at risk for it, explain why it produces particular symptoms, and develop interventions to try to reduce (...) its prevalence or the symptom severity. Of course, there are many situations in which one has, for practical reasons, only some of these desiderata; for example, control might be infeasible for technical or ethical reasons. But these remain, for many researchers, the ideal for why causal knowledge is a valuable end of scientific inquiry, including biological inquiry. There are, however, certain types of systems—in particular, chaotic systems—in which it appears that these ends are unattainable, and these systems appear to be widespread in the biological domain, broadly construed. In this paper, we will show why it is natural to think that causal models of chaotic systems cannot satisfy any of the three functions. But we will also show why this natural thought is wrong: we can have usable causal knowledge about even chaotic systems. Moreover, the ways in which we can have such knowledge lead us naturally to rethink a standard understanding of how causal learning and modeling proceed. In particular, just as we often must find the appropriate variables for a causal system, we also must determine the proper level or granularity of description for the dynamics of that system. (shrink)

In the framework of population dynamics, we start from the logistic equation describing the evolution of one species with limited food supply. A split device allows us to consider the population as two sub-populations x and y evolving analogously. The dynamical system has a one-parameter family of equilibria which is structurally unstable. Then small perturbations of the system (describing functional or ethological differentiations between the sub-species) lead in general to a new system involving a fast and a (...) slow dynamics with a finite number of equilibria. In simple situations where the differentiation is clearly either an advantage or an inconvenience for one of the subspecies, the stable equilibrium amounts to extinction of the disadvantaged subspecies (elementary Darwinism). Oppositely more complex differentiations (involving both advantages and inconveniences) often lead to stable equilibria with well-defined non zero proportions of the sub-populations (preservation of the biodiversity). Other examples are concerned with symbiosis-like differentiations, leading to preservation, whereas the opposite case (mutual nuisances) has an unstable equilibrium and lead to extinction of one or the other subspecies according to the initial conditions. The case of a scission into three subspecies is more rich in consequences. In certain cases, predator-prey relations lead to auto-organization phenomena with stable diversity-preserving diversity. Cases of instability are also possible, leading to orbits tending towards a poly-cycle.This implies some kind of pseudo-extinction: this amounts to “pseudo-periodic-like” orbits with “pseudo-periods” larger and larger, tending to infinity; each pseudo-period contains parts where one of the sub-populations practically vanish. Other non-linear perturbations lead to stable orbits. (shrink)

The aim of this work is to study complex ecological models exhibiting simple dynamics. We consider large scale systems which can be decomposed into weakly coupled subsystems. Perturbation Theory is used in order to get a reduced set of differential equations governing slow time varying global variables. As examples, we study the influence of the individual behaviour of animals in competition and predator-prey models. The animals are assumed to do many activities all day long such as searching for (...) food of different types. The degree of competition as well as the predation pressure are dependent upon these activities. Preys are more vulnerable when doing some activities during which they are very exposed to predators attacks rather than for others during which they are hidden. We study the effect of a change in the average individual behaviour of the animals on interspecific relationships. Computer simulations of the whole sets of equations are compared to simulations of the reduced sets of equations. (shrink)

Anticipatory acts or predictive behavior are prerequisites for living organisms to sustain their survival when escaping from a predator, catching prey, or schooling. For example, catching prey requires that the predator perform some procedures that are equivalent to estimating the directional movement of the prey, its speed and its distance relative to the predator. Underlying these procedures is time experience, which does not adhere to man-made mechanical clocks. Living organisms keep time based on the (...) local activities of each participant and form ecological clocks together. The timekeeping of ecological clocks has been called E-series time, which is interactive in character and consists of mutual alignment of timing that is co-adjusted to each other’s movements and rhythms. A main objective of our current work is to illustrate how E-series time is used for flows of anticipatory acts. To explain such predictive moves and their efforts based on how the perspective of the immediate future affects the present, we resort to the organismic activity of revising the preceding acts in retrospect and semiotic scaffolding that extends beyond simple linear causality. Special attention is paid to the construction of the notion of retrocausal scaffolding, which is a series of dialogical punctuations or mutual coordination of rhythms for the joint production of the present moment of now. Retrocausal scaffolding is synonymous with negotiated anticipation, which is a semiotic/communicative account of revising the preceding acts in the present moment. (shrink)

In this paper I consider the notion of “moral ecology” in relation to the social/cultural construction known as “narco-culture.” My claim is that the moral ecology of narco-culture is one that is both destructive and prohibitive of human flourishing. The general idea of a “moral ecology” is that the moral space of human conviviality is not unlike an ecological, or environmental, space—both are constituted by various interdependent relations which, when working harmoniously and in optimal capacity, maintain the overall well-being of (...) its inhabitants. Within non-human ecosystems, the quality or health of rivers, trees, earth, air, predator-prey relationships, etc., define what Allen Hertzke calls the system’s “carrying capacity.” The carrying capacity refers to what the system can handle while staying balanced and healthy and also indicates the point beyond which the system, if overburdened or degraded, begins to fall apart. In a social setting, the ecology is constituted by moral rules and behaviors, the degradation of which can cause the degradation of the entire system. (shrink)

This paper considers the implications of complex ecologic-economic dynamics for three broad, Post Keynesian perspectives: the uncertainty perspective, the macrodynamics perspective, and the Sraffian perspective. Catastrophic, chaotic, and other complex dynamics will be seen as reinforcing the conceptual foundations of Keynesian uncertainty. Predatory-prey models will be seen as deeply linked to Post Keynesian macrodynamic models. Finally, certain cases in ecologiceconomic systems will be seen as generating such Sraffian, capital theoretic conundra as reswitching. Ecologic-economic models considered besides predator-prey (...) will include fisheries, forestry, lake dynamics, and global climatic-economic dynamics. (shrink)

Volterra's (1926) equations for competition and predator-prey interactions are modified by introduction of root terms. A critical comparison with the original equations shows that the dynamic properties of the systems remain essentially alike, while the modification allows for explicit solution of the differential equations. Detailed solutions and numerical examples are given.

Diffusion plays an essential role in the distribution of predator and prey. We mainly research the diffusion network’s effect on the predator-prey model through bifurcation. First, it is found that the link probability and diffusion parameter can cause Turing instability in the network-organized predator-prey model. Then, the Turing stability region is obtained according to the sufficient condition of Turing instability and the eigenvalues’ distribution. Finally, the biological mechanism is explained through our theoretical results, which (...) are also illustrated by numerical simulation. (shrink)

According to Martha Nussbaum, treating animals justly is a matter of guaranteeing each individual those capabilities up to a minimum threshold that are essential for flourishing as a member of a particular species. Nussbaum’s basic theoretical framework is acceptable; however, a capability which Nussbaum thinks is not essential for the flourishing, the oppor­tunity to kill as a part of exercising predatory instinct, may in fact be essential for predator flourishing. Nussbaum ought to be concerned with the possibility that this (...) capability is essential, since if it is, it is likely that in doing less harm than good we will also be treating some predators unjustly by denying them the opportunity to flourish. (shrink)

In this paper I propose a reinforcement learning model for a predator preying upon two types of prey, the unpalatable (noxious) models, and the palatable mimics. The latter type of prey resembles the models in appearance so as to derive some protection from the predator who must avoid the unpalatable models. Essentially the predator is treated as a learning automaton adopting a simple reinforcement learning strategy in order to increase its consumption of palatable prey (...) and reduce the consumption of unpalatable ones. The populations of both mimics and models are assumed to grow logistically. (shrink)