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.
Petrovskii
S V
SV
Shirshov Institute of Oceanology, Russian Academy of Sciences, Nakhimovsky Prospect 36, Moscow, 117218, Russia. spetros@sio.rssi.ru
Malchow
H
H
D000818:Animals; D001522:Behavior, Animal; D003198:Computer Simulation; D008954:Models, Biological; D017711:Nonlinear Dynamics; D011157:Population Dynamics; D011235:Predatory Behavior