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 two reaction- diffusion equations with biologically reasonable non-linearities (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