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Wave of chaos: New mechanism of pattern formation in spatio-temporal population dynamics. (English) Zbl 1035.92046
Summary: The dynamics of a simple prey-predator system is described by a system of two reaction-diffusion equations with biologically reasonable nonlinearities (logistic growth of the prey, Holling type II functional response of the predator). We show that, when the local kinetics of the system is oscillatory, for a wide class of initial conditions the evolution of the system leads to the formation of a non-stationary irregular pattern corresponding to spatio-temporal chaos. The chaotic pattern first appears inside a sub-domain of the system. This sub-domain then steadily grows with time and, finally, the chaotic pattern invades the whole space, displacing the regular pattern.

MSC:
92D40Ecology
92D25Population dynamics (general)
92C15Developmental biology, pattern formation
37N25Dynamical systems in biology
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References:
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