SIMULATION ANALYSIS OF SPATIO-TEMPORAL PATTERNS IN STOCHASTIC PLANKTON-FISH SYSTEMS

An ecosystem consists of a large variety of species and creatures interact with each other by means of a food chain. Since behaviors of some species in the food chain have an effect on the whole ecosystem, it is very important to consider spatio-temporal change of the populations of species from the view point of ecosystem management and protection. In this paper, we consider the food chain consisting of three populations, fish, zooplankton and phytoplankton, and study the modeling of such a food chain and analyze their spatio-temporal behaviors by numerical simulations. Environmental changes in the food web cause some kinds of random fluctuations in the growth and the death rates of species. In order to study the impact of these uncertainties on the food chain, we need the stochastic model. Thus, we propose the stochastic plankton-fish model. In the numerical analyses of the stochastic plankton-fish system, we show that the size, motion and geometrical shape of fish school have a great influence on emergence of a spiral wave in the plankton-fish system and such a spiral is robust for disturbance.