Pattern formation of a spatial predator-prey system

There are random and directed movements of predator and prey populations in many natural systems which are strongly influenced and modified by spatial factors. To investigate how these migration (directed movement) and diffusion (random movement) affect predator-prey systems, we have studied the spatiotemporal complexity in a predator-prey system with Holling-Tanner form. A theoretical analysis of emerging spatial pattern is presented and wavelength and pattern speed are calculated. At the same time, we present the properties of pattern solutions. The results of numerical simulations show that migration has prominent effect on the pattern formation of the population, i.e., changing Turing pattern into traveling pattern. This study suggests that modelling by migration and diffusion in predator-prey systems can account for the dynamical complexity of ecosystems.