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Chaos in one-predator, two-prey models: General results from bifurcation theory. (English) Zbl 0802.92017
Summary: 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.

MSC:
92D25Population dynamics (general)
37N99Applications of dynamical systems
34C23Bifurcation (ODE)
37D45Strange attractors, chaotic dynamics
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References:
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