A minimal model of pattern formation in a prey-predator system. (English) Zbl 0990.92040

Petrovskii, S. V.; Malchow, Horst

Math. Comput. Modelling 29, No. 8, 49-63 (1999).

Summary: The spatio-temporal dynamics of a prey-predator community is described by two reaction-diffusion equations. It is shown that for a class of initial conditions the spatio-temporal system dynamics resembles a “phase transition” between a regular and an irregular phase, separated by a moving boundary. A simple approach to specify spatio-temporal chaos is proposed.

MSC:

92D40	Ecology
35K57	Reaction-diffusion equations
37N25	Dynamical systems in biology

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