Chaos in one-predator, two-prey models: general results from bifurcation theory.
We show that chaos is the expected outcome of the dynamics of a class of one-predator, two-prey models. This generalizes results of previous studies of Lotka-Volterra models. We examine dynamics near a state in which a high codimension bifurcation occurs, considering all possible nearby dynamics in both parameter and state space by doing an unfolding analysis of the model's normal form. In this way, we argue that realistic predator-prey systems that can be closely modeled by the general models discussed here must exhibit chaotic dynamics.
Klebanoff
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Institute of Theoretical Dynamics, University of California, Davis 95616.
Hastings
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D000818:Animals; D008960:Models, Psychological; D017711:Nonlinear Dynamics; D011235:Predatory Behavior