Wave of chaos: New mechanism of pattern formation in spatio-temporal population dynamics

The dynamics of a simple prey-predator system is described by a system of t wo reaction-diffusion equations with biologically reasonable non-linearitie s (logistic growth of the prey, Holling type II functional response of the predator). We show that, when the local kinetics of the system is oscillato ry, for a wide class of initial conditions the evolution of the system lead s to the formation of a non-stationary irregular pattern corresponding to s patio-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 patter n, (C) 2001 Academic Press.