The aim of this paper is to provide a mathematical basis for the plausible idea that regular dynamical laws can only produce (quickly and reliably) regular structures. Thus the actual laws, which are regular, can only produce regular objects, like crystals, and not irregular ones, like living organisms.

In recent debates mechanisms are often discussed in the context of ‘complex systems’ which are understood as having a complicated compositional structure. I want to draw the attention to another, radically different kind of complex system, in fact one that many scientists regard as the only genuine kind of complex system. Instead of being compositionally complex these systems rather exhibit highly non-trivial dynamical patterns on the basis of structurally simple arrangements of large numbers of non-linearly interacting constituents. The characteristic dynamical (...) patterns in what I call “dynamically complex systems” arise from the interaction of the system’s parts largely irrespective of many properties of these parts. Dynamically complex systems can exhibit surprising statistical characteristics, the robustness of which calls for an explanation in terms of underlying generating mechanisms. However, I want to argue, dynamically complex systems are not sufficiently covered by the available conceptions of mechanisms. I will explore how the notion of a mechanism has to be modified to accommodate this case. Moreover, I will show under which conditions the widespread, if not inflationary talk about mechanisms in complex systems stretches the notion of mechanisms beyond its reasonable limits and is no longer legitimate. (shrink)

This paper examines the rising competition between computational and dynamic conceptualizations of complexity in economics. While computable economics views the complexity as something rigorously defined based on concepts from probability, information, and computability criteria, dynamic complexity is based on whether a system endogenously and deterministically generates erratically dynamic behavior of certain kinds. On such behavior is the phenomenon of emergence, the appearance of new forms or structures at higher levels of a system from processes (...) occurring at lower levels. While the two concepts can overlap, they represent substantially different perspectives. A competition of sorts between them may become more important as new, computerized market systems emerge and evolve to higher levels of complexity of both kinds. (shrink)

The paradigm of Laplacean determinism combines three regulative principles: determinism, predictability, and the explanatory adequacy of universal laws together with purely local conditions. Historically, it applied to celestial mechanics, but it has been expanded into an ideal for scientific theories whose cogency is often not questioned. Laplace’s demon is an idealization of mechanistic scientific method. Its principles together imply reducibility, and rule out holism and emergence. I will argue that Laplacean determinism fails even in the realm of planetary dynamics, and (...) that it does not give suitable criteria for explanatory success except within very well defined and rather exceptional domains. Ironically, the very successes of Laplacean method in the Solar System were made possible only by processes that are not themselves tractable to Laplacean methodology. The results of some of these processes were first observed in 1964, and violate the Lapacean requirements of locality and predictability, opening the door to holism and nonreducibility, i.e., emergence. Despite the falsification of Laplacean methodology, the explanatory resources of holism and emergence remain in scientific limbo, though emergence has been used somewhat indiscriminately in recent scientific literature. I make some remarks at the end about the proper use of emergence in its traditional sense going back to C.D. Broad. (shrink)

We prove that any speedable computably enumerable set may be split into a disjoint pair of speedable computably enumerable sets. This solves a longstanding question of J.B. Remmel concerning the behavior of computably enumerable sets in Blum's machine independent complexity theory. We specify dynamic requirements and implement a novel way of detecting speedability-by embedding the relevant measurements into the substage structure of the tree construction. Technical difficulties in satisfying the dynamic requirements lead us to implement "local" strategies (...) that only look down the tree. The (obvious) problems with locality are then resolved by placing an isomorphic copy of the entire priority tree below each strategy (yielding a self-similar tree). This part of the construction could be replaced by an application of the Recursion Theorem, but shows how to achieve the same effect with a more direct construction. (shrink)

The aim of this book is to show how supramolecular complexity of cell organization can dramatically alter the functions of individual macromolecules within a cell. The emergence of new functions which appear as a consequence of supramolecular complexity, is explained in terms of physical chemistry. The book is interdisciplinary, at the border between cell biochemistry, physics and physical chemistry. This interdisciplinarity does not result in the use of physical techniques but from the use of physical concepts to study (...) biological problems. In the domain of complexity studies, most works are purely theoretical or based on computer simulation. The present book is partly theoretical, partly experimental and theory is always based on experimental results. Moreover, the book encompasses in a unified manner the dynamic aspects of many different biological fields ranging from dynamics to pattern emergence in a young embryo. The volume puts emphasis on dynamic physical studies of biological events. It also develops, in a unified perspective, this new interdisciplinary approach of various important problems of cell biology and chemistry, ranging from enzyme dynamics to pattern formation during embryo development, thus paving the way to what may become a central issue of future biology. (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)

Unified and causal complex-dynamic origin of standard (special and general) relativistic and quantum effects revealed previously at the lowest levels of world interaction dynamics is explicitly generalised to all higher levels of unreduced interaction processes, thus additionally confirming the causally complete character of complex-dynamical, naturally quantised relativity, which does not contain any artificially added, abstract postulates. We demonstrate some elementary applications of this generalised quantum relativity at higher levels of complex brain and social interaction dynamics.

Systemic therapy considers the complex dynamics of relational factors and resources contributing to psychological symptoms. Negative maintaining factors have been well researched for people suffering from Alcohol-use Disorders. However, we know little about the complex dynamics of these negative factors and resources. We interviewed fifty-five participants suffering or fully remitted from Alcohol-use disorders in this cross-sectional study. The interviews focused on relational factors referring to a Support Social Network and a Craving Social Network. The CSN included all significant others who (...) were associated with craving situations. We compared the network characteristics of the group suffering from Alcohol-use Disorders to a fully remitted control group. The abstinent group with full remission named on average fewer individuals in the CSNs. They had lower social negativity mean scores in the Support Social Network compared to the non-remitted group. In the CSN, the mean scores of social support were significantly higher than the median for both groups. These findings reveal the complex interplay of relational patterns contributing to the etiology, maintenance, and recovery from Alcohol-use disorders. A successful recovery can be linked to increased social resources and reduced relations associated with craving. However, craving-associated relations represent an important source of social support. Future research should investigate this ambivalence for the systemic perspective on the explanation and treatment of Alcohol-use disorders. (shrink)

This book reports recent landmark developments and the state of the art in NDS science in psychological theory and research.

Even beginners and young graduate students will have something to learn from this book." (Andre Hautot, Physicalia, Vol. 57 (3), 2005)"All-in-all, this highly ...

In this paper, a fresh shear-displacement model is developed for the plastic deformation of the bulk metallic glasses. The multiscale behavior in the shear banding process and the dynamics transition with the parameters are investigated in analytical form. We present a theoretical support for the transition from unstable states to stable states in the experiment by multiscale analysis and the stability analysis. With the small parameter increasing from negative to positive, the stability of the shear slipping displacement system changes, and (...) there is a limit cycle at the transition stage. Meanwhile, the phase diagram and the power spectrum also suggest that there is dynamics transition with the parameter changing. Moreover, the complexity is analyzed for different disturbance parameters, and it is coincident with the fact that the solution is more irregular for larger disturbance. In addition, we find that the amplitude of solution decreases with the temperature decreasing, which is consistent with the experimental results that the amplitude of the serration is smaller and smaller as the temperature decreases. (shrink)

Complex dynamical systems theory is an evolution of nonlinear dynamics, developed for modeling and simulation of biological systems. Here, we speculate on the potential of this strategy for the emerging theory of social systems, and the implications for the future of our own planetary society.

An extended analysis compared to observations shows that modern “globalised” world civilisation has passed through the invisible “complexity threshold”, after which usual “spontaneous”, empirically driven kind of development (“invisible hand” etc.) cannot continue any more without major destructive tendencies. A much deeper, non-simplified understanding of real interaction complexity is necessary in order to cope with such globalised world development problems. Here we introduce the universal definition, fundamental origin, and dynamic equations for a major related quantity of (systemic) (...) risk characterising real complex system development tendencies at any level of dynamics. Practically important conclusions are derived, opening further detailed applications in economy, finance and development practice. (shrink)

Understanding the dynamics of complex ecosystems is a necessary step to maintain and control them. Yet, reverse-engineering ecological dynamics remains challenging largely due to the very broad class of dynamics that ecosystems may take. Here, this challenge is tackled through symbolic regression, a machine learning method that automatically reverse-engineers both the model structure and parameters from temporal data. How combining symbolic regression with a “dictionary” of possible ecological functional responses opens the door to correctly reverse-engineering ecosystem dynamics, even in the (...) case of poorly informative data, is shown. This strategy is validated using both synthetic and experimental data, and it is found that this strategy is promising for the systematic modeling of complex ecological systems. (shrink)

A generalization of a Burridge-Knopoff spring-block model is investigated to illustrate the dynamics of transform faults. The model can undergo Hopf bifurcation and fold bifurcation of limit cycles. Considering the cyclical nature of the spring stiffness, the model with periodic perturbation is further explored via a continuation technique and numerical bifurcation analysis. It is shown that the periodic perturbation induces abundant dynamics, the existence, the switch, and the coexistence of multiple attractors including periodic solutions with various periods, quasiperiodic solutions, chaotic (...) solutions through torus destruction, or cascade of period doublings. Throughout the results obtained, one can see that the system manifests complex dynamical behaviors such as chaos, self-organized criticality, and the transition of dynamical behaviors when it comes to periodic perturbations. Even very small variation of a parameter can result in radical changes of the dynamics, which provides a new insight into the fault dynamics. (shrink)

The past two decades have seen an explosion in the methods and directions of neuroscience research. Along with many others, complexity research has rapidly gained traction as both an independent research field and a valuable subdiscipline in computational neuroscience. In the past decade alone, several studies have suggested that psychiatric disorders affect the spatiotemporal complexity of both global and region-specific brain activity (Liu et al., 2013; Adhikari et al., 2017; Li et al., 2018). However, many of these studies (...) have not accounted for the distributed nature of cognition in either the global or regional complexity estimates, which may lead to erroneous interpretations of both global and region-specific entropy estimates. To alleviate this concern, we propose a novel method for estimating complexity. This method relies upon projecting dynamic functional connectivity into a low-dimensional space which captures the distributed nature of brain activity. Dimension-specific entropy may be estimated within this space, which in turn allows for a rapid estimate of global signal complexity. Testing this method on a recently acquired obsessive-compulsive disorder dataset reveals substantial increases in the complexity of both global and dimension-specific activity versus healthy controls, suggesting that obsessive-compulsive patients may experience increased disorder in cognition. To probe the potential causes of this alteration, we estimate subject-level effective connectivity via a Hopf oscillator-based model dynamic model, the results of which suggest that obsessive-compulsive patients may experience abnormally high connectivity across a broad network in the cortex. These findings are broadly in line with results from previous studies, suggesting that this method is both robust and sensitive to group-level complexity alterations. (shrink)

The subject of this chapter is the identity of individual dynamical objects and properties. Two problems have dominated the literature: transtemporal identity and the relation between composition and identity. Most traditional approaches to identity rely on some version of classification via essential or typical properties, whether nominal or real. Nominal properties have the disadvantage of producing unnatural classifications, and have several other problems. Real properties, however, are often inaccessible or hard to define (strict definition would make them nominal). I suggest (...) that classification should be in terms of dynamical properties of systems, starting with individual systems rather than classes, and working up by abstractions that fit causal generalities. The advantage of this approach is that individuality is testable and revisable as we come to know more about systems. Another advantage is that if anything is real, then it is the dynamical. Once I have presented this approach in general, I will show that the central concept of dynamical cohesion (the "dividing glue") is amenable to giving a principled account of individuation as a process, at the same time explaining the origin of diversity. Some other advantages of this approach are presented, including how it can be used as a basis for testable classifications. This last has moral implications, since cohesion at the individual and the social levels, and their interactions, can impinge on proper moral decisions. (shrink)

The problem of stability in population dynamics concerns many domains of application in demography, biology, mechanics and mathematics. The problem is highly generic and independent of the population considered (human, animals, molecules,…). We give in this paper some examples of population dynamics concerning nucleic acids interacting through direct nucleic binding with small or cyclic RNAs acting on mRNAs or tRNAs as translation factors or through protein complexes expressed by genes and linked to DNA as transcription factors. The networks made of (...) these interactions between nucleic acids (considered respectively as edges and nodes of their interaction graph) are complex, but exhibit simple emergent asymptotic behaviours, when time tends to infinity, called attractors. We show that the quantity called attractor entropy plays a crucial role in the study of the stability and robustness of such genetic networks. (shrink)

Most of us came into ecology with memories of special personal places. A cliff top that Claude Monet might have painted. Allen as a youth spent his holidays on the Dorset Coast near Swanage; he can still smell the sea breeze of his childhood. Curtin grow up on a farm in southwestern Wisconsin, the dew of the grass and the bright green on a June morning remains vivid. The catching of reptiles and insects for him awakened a curiosity about the (...) natural world that has remained to this day. But once into the field there came the scholarship. With ever tighter grant monies, the pressure to publish takes so much of the fun out of it. A climate of unbridled careerism prevails and shows itself in the incremental state of the literature: little things to list on this year's activities report. There are now even predatory journals that cynically do not seriously review submissions, and only collect page charges. As journal editors have a desperate time getting reviews done by mature scholars, instead of a hand off to their overworked graduate students. So what is to be done - how can we bring the joy and importance of discovery back into it all? After all ecology is done by human beings. Mostly it is a personal mission, for what great ecologists write is frequently personal and life changing. So an undercurrent of this book is to remind and reveal the original purpose of science. Not professional advancement, but the genuine search for novel ideas and the imperative to share hard won insights and personal passions. (shrink)

distraction that leads innocent Post Keynesians into “classical sin.” Davidson (1994, 1996) argues that core Post Keynesian (PK) ideas such as that insufficient aggregate demand arise from fundamental uncertainty in a monetary economy do not depend on nonlinearity or complexity, that these core concepts are axiomatically and ontologically true, and that the inability of agents to forecast well in dynamically complex situations reflects mere epistemological problems of insufficient computational abilities. Thus complex dynamics is merely a classical stalking horse. This (...) writer (Rosser, 1990, 1998, 2001) disagrees with the argument presented above and its relatives (Mirowski, 1990; Carrier, 1993). Dynamic complexity provides a foundation for fundamental uncertainty in Keynesian and PK models, and this applies to most of the various sub-branches of PKE besides Davidson’s “fundamentalist” or “Keynes-Post Keynesian”2 approach. The argument will be considered regarding three subdivisions of Post Keynesianism as identified by Hamouda and Harcourt (1988): the aforementioned fundamentalist Keynesianism, Sraffian (or neo-Ricardian), and Kaleckian (or Kaleckian- Robinsonian).3 Following King (2002, chap. 10), I admit to being more in sympathy with those he describes as “synthesizers” than with the more partisan sectarians of these approaches.4 I shall describe how each sub-branch has been analyzed using ideas of.. (shrink)

The contemporary process of financialization has been a major driver of the remarkable changes witnessed in global food and agricultural markets over the past decade, contributing to the rise and subsequent volatility of food and agricultural commodity prices since 2006. In the wake of these developments it has become clear that the turmoil has intensified the relationship between agriculture and finance in ways that have profound and enduring implications for the sector, and the people whose lives and livelihoods depend upon (...) it. This symposium brings together four original research articles that contemplate the contemporary relationship between the agrifood and financial sectors. They examine a variety of overlapping themes, including the creation of financial assets from farmland and agricultural commodities, the activities of different types of investors in these assets in specific geographic contexts, and the challenges of governing this activity at the global scale. These articles show that the period of market volatility that began a decade ago re-invigorated investor interest in financial products linked to agriculture and farming, and inspired the packaging of new forms of financial assets in ways that have affected politics and practice on the ground, and are likely to leave a lasting legacy. (shrink)

This work presents a post-positivist research framework for explaining any surprising or anomalous fact in the evolutionary path of a complex, dynamic, and contingent social process. Firstly, it elaborates on the reconciliation betweenthe ontological and epistemological assumptions of Critical Realism with the principles of American Pragmatism. Next, the research method is presented: theoretical propositions about a social structure are translated into a set of grammar rules that acknowledge patterns of sequences of events, either involving individual action or interaction between (...) actors within a real social system. The result is a discrete mathematical model for a concrete category of social process based on these rules. Finally, data-grounded refinement of the theory is possible through comparison between cases belonging to the same category, but differing in some contingent pattern of sequences of event outcomes. Consequently, their grammars differ in some pairs of context-sensitive rules that explain this surprising fact, and the derivation of this alternative historical trajectory of event outcomes becomes an extension to the early category of social process. In this sense, the proposed framework suggests a hierarchy of classes of grammars for middle-range explanations based on the ontological assumption of the generative nature of social reality. (shrink)

L. Hardy has formulated an axiomatization program of quantum mechanics and generalized probability theories that has been quite influential. In this paper, properties of typical Hamiltonian dynamical systems are used to argue that there are applications of probability in physical theories of systems with dynamical complexity that require continuous spaces of pure states. Hardy’s axiomatization program does not deal with such theories. In particular Hardy’s fifth axiom does not differentiate between such applications of classical probability and quantum probability.

The dynamic models are proposed to investigate the influence node activity has on rumor spreading process in both homogeneous and heterogeneous networks. Different from previous studies, we believe that the activity of nodes in complex networks affects the process of rumor spreading. An active node can have contact with all the nodes it directly links to, while an inactive node could only interact with its active neighbors. We explore the joint effort of activity rate, spreading rate and network topology (...) on rumor spreading process by mean-field equations and numerical simulations, which reveals that there exists a critical curve consisting of critical activity rate and spreading rate; meanwhile, activity rate and spreading rate both have influence on the final rumor spreading scale. (shrink)

Social network analysis has gained increasing academic attention in the construction domain over the past two decades due to its capability to characterize the complexity and dynamics of interindividual and interorganizational interactions. To date, however, scant attempt has been made to develop an integrated framework to systematically review the diversified network research at different levels in this domain and to quantitatively characterize the evolution of related research interests and research instruments. This study aims to fill this gap by conducting (...) a bibliometric-qualitative review based on 106 papers published from 1997 to 2020. Keyword cooccurrence analysis is employed to reveal the research foci, identify the research trends, and develop a comprehensive categorization framework, which classifies related research based on two interrelated dimensions: the type of network node and the levelof network analysis. The framework then facilitates further content analysis in terms of research topics, research designs, and research instruments. The results provide evidence that the research foci in this domain are generally moving towards addressing the complexity and dynamics of project-related relations at more diversified levels, in terms of not only research topics but also research instruments. Future research can be enriched by investigating the multiple types of dynamic interproject relationships, adopting state-of-the-art methodologies for network data collection and triangulation, and employing multiple SNA constructs and inferential statistical methods to reveal how complex networks coevolve and interact with actors’ behaviors as well as project and organizational outcomes. (shrink)

In recent years, the method of the complex network has been applied to various fields. Dynamics research in complex networks is also an important branch. There are many types of research into dynamic complex network, but few scholars use bibliometrics to study it. Therefore, this paper adopts the method of bibliometrics to analyze the development history and status quo of dynamic complex network, providing a summary description of this research field. We used CiteSpace and Pajek to analyze 2936 (...) relevant papers on the website of Web of Science and further interpreted and summarized the analysis results. To fully show the bibliometric results, we further derive the productive countries, institutions, sources, and authors and some main research directions in the dynamic complex network research. The research results show that the dynamic complex network research method was applied to various fields after the dynamic research method had been integrated into the complex network. According to the subject analysis of the cited papers, we find that the dynamic complex network method has been widely used in various subjects. Through emergent analysis, we found that the latest hot research trends are the study of infectious diseases and applications in neural networks. At the same time, through the main path analysis, we find the essential literature to elaborate on the development context of a dynamic complex network at different time points. This paper gives a comprehensive analysis of dynamic complex network research and provides some enlightenment for the future research direction. (shrink)

A summary of topics and theoretical approaches to dynamical systems and psychology. Includes chapters on physical systems, self-organization, state space and dimensionality, networks, neurodynamics, fractals and how such concepts help to explain cognition and the mind.

Various complex dynamics in ecologic-economic systems are presented with an emphasis upon models of global warming dynamics and fishery dynamics. Chaotic and catastrophic dynamic patterns are shown to be possible, along with other complex dynamics arising from nonlinearities in such combined systems. Problems associated with amplified oscillations due to these nonlinear interactions in the combined interactions of human economic decisionmaking with ecological dynamics are identified and discussed. Implications for policy are examined with strong recommendations for greater emphasis in particular (...) upon the precautionary principle to avoid catastrophic collapses beyond critical thresholds and the scale-matching principle to ensure that efforts to manage complex nonlinear dynamics are directed at the appropriate levels of ecologiceconomic interaction. Key Words: complex dynamics, chaos, catastrophe, fisheries, global warming.. (shrink)

Theory of mind refers to the human capacity for reasoning about others’ mental states based on observations of their actions and unfolding events. This type of reasoning is notorious in the cognitive science literature for its presumed computational intractability. A possible reason could be that it may involve higher-order thinking. To investigate this we formalize theory of mind reasoning as updating of beliefs about beliefs using dynamic epistemic logic, as this formalism allows to parameterize ‘order of thinking.’ We prove (...) that theory of mind reasoning, so formalized, indeed is intractable. Using parameterized complexity we prove, however, that the ‘order parameter’ is not a source of intractability. We furthermore consider a set of alternative parameters and investigate which of them are sources of intractability. We discuss the implications of these results for the understanding of theory of mind. (shrink)

The logic of genetic discovery has changed little over time, but the focus of biology is shifting from simple genotype–phenotype relationships to complex metabolic, physiological, developmental, and behavioral traits. In light of this, the traditional reductionist view of individual genes as privileged difference‐making causes of phenotypes is re‐examined. The scope and nature of genetic effects in complex regulatory systems, in which dynamics are driven by regulatory feedback and hierarchical interactions across levels of organization are considered. This review argues that it (...) is appropriate to treat genes as specific actual difference‐makers for the molecular regulation of gene expression. However, they are often neither stable, proportional, nor specific as causes of the overall dynamic behavior of regulatory networks. Dynamical models, properly formulated and validated, provide the tools to probe cause‐and‐effect relationships in complex biological systems, allowing to go beyond the limitations of genetic reductionism to gain an integrative understanding of the causal processes underlying complex phenotypes. (shrink)

This paper analyzes the complex historical and regional factors that contribute to the escalation of destruction from 2003 on in Darfur. Darfur is not an isolated case that suddenly erupted in violence. It is the most recent case in a long history of repeated violations by the Sudanese state against its citizens. From the use of proxy militias (the Janjaweed) to signing peace agreements that fragment and weaken the opposition, destruction in Darfur continues government strategies of divide and rule. At (...) the same time, complex regional dynamics especially between Sudan, Chad and the Central African Republic add to violence and instability within states and across borders. The paper emphasizes the speed with which during 2003–2005 over 2.4 million were uprooted from their homes and the ongoing vulnerability of internally displaced persons to attacks, disease and malnutrition. This restructuring of the population in Darfur is part of a strategy to control the populace and redistribute land and other resources. The multicausal origin of the conflict and its increasing complexity points to the difficulty of providing security for the people in Darfur and resolving the conflict. (shrink)

This paper presents a view of the process of transition from planned command socialism to mixed market capitalism involving nonlinear complex dynamical phenomena. After the former institutional structure disappears a coordination failure can bring about macroeconomic collapse as in almost all of the former Soviet bloc or macroeconomic boom as in China. A closely linked phenomenon is the rise of the underground economy as inflation and income inequality increase. This can lead to a jump from one equilibrium to a very (...) different one as nonlinear social feedback processes operate in the transition. (shrink)

This paper presents a view of the process of transition from planned command socialism to mixed market capitalism involving nonlinear complex dynamical phenomena. After the former institutional structure disappears a coordination failure can bring about macroeconomic collapse as in almost all of the former Soviet bloc or macroeconomic boom as in China. A closely linked phenomenon is the rise of the underground economy as inflation and income inequality increase. This can lead to a jump from one equilibrium to a very (...) different one as nonlinear social feedback processes operate in the transition. (shrink)

Covering a broad range of topics, this text provides a comprehensive survey of the modelling of chaotic dynamics and complexity in the natural and social sciences. Its attention to models in both the physical and social sciences and the detailed philosophical approach make this an unique text in the midst of many current books on chaos and complexity. Including an extensive index and bibliography along with numerous examples and simplified models, this is an ideal course text.