David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Acta Biotheoretica 51 (3):189-222 (2003)
The dynamics of single populations up to ecosystems, are often described by one or a set of non-linear ordinary differential equations. In this paper we review the use of bifurcation theory to analyse these non-linear dynamical systems. Bifurcation analysis gives regimes in the parameter space with quantitatively different asymptotic dynamic behaviour of the system. In small-scale systems the underlying models for the populations and their interaction are simple Lotka-Volterra models or more elaborated models with more biological detail. The latter ones are more difficult to analyse, especially when the number of populations is large. Therefore for large-scale systems the Lotka-Volterra equations are still popular despite the limited realism. Various approaches are discussed in which the different time-scale of ecological and evolutionary biological processes are considered together.
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Pierre Auger & Jean-Christophe Poggiale (1996). Aggregation and Emergence in Hierarchically Organized Systems: Population Dynamics. Acta Biotheoretica 44 (3-4):301-316.
P. Tracqui (1994). Organizing Centres and Symbolic Dynamic in the Study of Mixed-Mode Oscillations Generated by Models of Biological Autocatalytic Processes. Acta Biotheoretica 42 (2-3):147-166.
Peter Richerson, Homage to Malthus, Ricardo, and Boserup: Toward a General Theory of Population, Economic Growth, Environmental Deterioration, Wealth, and Poverty.
Peter Antonelli & Pierre Auger (1995). Corals and Starfish Devastation of the Great Barrier Reef: Aggregation Methods. Acta Biotheoretica 43 (4):481-493.
J.-P. Françoise & C. Piquet (2005). Hysteresis Dynamics, Bursting Oscillations and Evolution to Chaotic Regimes. Acta Biotheoretica 53 (4).
Jean-Christophe Poggiale, Pierre Auger & Robert Roussarie (1995). Perturbations of the Classical Lotka-Volterra System by Behavioral Sequences. Acta Biotheoretica 43 (1-2):27-39.
Majid Bani-Yaghoub & David E. Amundsen (2008). Study and Simulation of Reaction–Diffusion Systems Affected by Interacting Signaling Pathways. Acta Biotheoretica 56 (4):315-328.
Pierre M. Auger & Robert Roussarie (1994). Complex Ecological Models with Simple Dynamics: From Individuals to Populations. Acta Biotheoretica 42 (2-3):111-136.
M. Arrigoni & A. Steiner (1983). Square-Root Models for the Volterra Equations and the Explicit Solution of These Models. Acta Biotheoretica 32 (2):123-142.
Eva Sánchez, Rafael Bravo Parra & Pierre Auger (1995). Linear Discrete Models with Different Time Scales. Acta Biotheoretica 43 (4).
Added to index2009-01-28
Total downloads5 ( #242,321 of 1,168,113 )
Recent downloads (6 months)0
How can I increase my downloads?