Simulation Analyses of Behaviours of Spatially Extended Predator-Prey Systems with Random Fluctuations

We often observe some kind or another of random fluctuations in physical, chemical and social phenomena to a greater or lesser extent. The analysis of influence of such fluctuations on phenomena is very important as a basic problem in various fields including design and planning of controlled systems in control engineering and analysis of option pricing in economics. In this paper, focusing on biological communities, we study the influence of the random fluctuations on predator-prey systems with diffusion. Noting that interaction of phytoplankton and zooplankton is the basis of a food chain in the lake and the ocean, we consider the two-species predator-prey systems consists of phytoplankton and zooplankton. We analyze the influence of the random fluctuations on the spatio-temporal patterns generated by phytoplankton and zooplankton by the numerical simulations.