Phytoplankton Zooplankton system with bounded random parameter

The aim of this work is to use the Chebyshev orthogonal polynomial approximation method to analyze the stochastic nonlinear dynamical systems with bounded random parameter. Consider a prey - predator model describing the time evolution of phytoplankton-zooplankton populations in an open environment. This stochastic phytoplankton zooplankton system (SPZ system for short) is transformed by the Chebyshev orthogonal polynomial approximation method into an equivalent deterministic system, whose responses can be readily obtained by conventional numerical methods. In this way we can explore plenty of stochastic dynamical phenomenons of the SPZ system by some deterministic nonlinear dynamical methods.