Abstract
Since each creature interacts with each other through a food chain, an analysis of the food chain is a crucial problem in an ecosystem. In this paper, we consider the plankton-fish system consisting of fish, zooplankton and phytoplankton, and study the influence of the random noise on the stability of the plankton system under fish school by numerical simulations. The qualitative change of the solutions of differential equations by variation of a system parameter is generally called a bifurcation. This paper is concerned with the bifurcation analysis of a stochastic plankton-fish system. As major analytical methods for the stochastic bifurcation, the P-bifurcation (Phenomenological bifurcation) and the D-bifurcation (Dynamical bifurcation) approaches are cited. The P-bifurcation studies a stationary measure corresponding to the one-point motion, while the D-bifurcation considers the stability of invariant measures. Since the P-bifurcation approach is based on the one point-motion, there is a possibility to miss certain branches in bifurcation diagrams. So, we study the bifurcation in the stochastic plankton-fish system using the D-bifurcation. By the numerical simulations, we show that the D-bifurcation does not occur in the stochastic plankton-fish system considered here.
