Dynamics of a stochastic phytoplankton-toxic phytoplankton-zooplankton
system under regime switching
Abstract
In this paper, a stochastic phytoplankton-toxic
phytoplankton-zooplankton system with Beddington-DeAngelis functional
response, where both the white noise and regime switching are taken into
account, is studied analytically and numerically. The aim of this
research is to study the combined effects of the white noise, regime
switching and toxin-producing phytoplankton (TPP) on the dynamics of the
system. Firstly, the existence and uniqueness of global positive
solution of the system is investigated. Then some sufficient conditions
for the extinction, persistence in the mean and the existence of a
unique ergidoc stationary distribution of the system are derived.
Significantly, some numerical simulations are carried to verify our
analytical results, and show that high intensity of white noise is
harmful to the survival of plankton populations, but regime switching
can balance the different survival states of plankton populations and
decrease the risk of extinction. Additionally, it is found that an
increase in the toxin liberation rate produced by TPP will increase the
survival change of phytoplankton, while it will reduce the biomass of
zooplankton. All these results may provide some insightful understanding
on the dynamics of phytoplankton-zooplankton system in randomly
disturbed aquatic environments.