Modelling the spatiotemporal dynamics of diffusive prey-predator interactions: Pattern formation and ecological implications

Abstract

In this paper, we investigate the formation of spatiotemporal patterns in ecological systems via numerical simulations. We study the diffusive prey-predator model and observe the rich dynamical structure as a result of prey- predator interactions in one and two spatial dimensions. In 1-d numerical investigations we show that, for a large class of initial conditions, the evolution of the model leads to the emergence of non-stationary irregular patterns, given that the local kinetics of the system is oscillatory. This corresponds to spatiotemporal chaos. The irregular patterns first emerge inside a subdomain of the system. This subdomain then steadily grows with time and, finally, the irregular chaotic patterns invade the whole space, displacing the regular pattern. For 2-d numerical simulations we observed the formation of spiral waves, patchy structures, spiral defect chaos and spatiotemporal chaos due to Turing instability in our prey-predator model. These two-dimensional patterns are very beautiful and very interesting to be observed and interpreted from the ecological point of view.