Dynamics of a stochastic phytoplankton–zooplankton system with defensive and offensive effects

In this paper, we propose a stochastic phytoplankton–zooplankton system considering phytoplankton defensive and zooplankton offensive effects. The aim of this paper is to study the effects of environmental fluctuations on plankton population dynamics. We prove the existence, uniqueness and stochastically ultimately boundedness of global positive solutions, and the extinction and persistence in the mean of plankton populations. When the system is persistent in the mean, there exists a unique stationary distribution. To further investigate the dynamics of the stochastic plankton system, we perform some numerical simulations and find that the white noise can directly affect the survival of plankton populations. The phytoplankton defense can strengthen the capability of phytoplankton protection that will benefit the plankton survival and weaken the impact of environmental fluctuations, but it has a negative effect on zooplankton population. Our findings reveal that zooplankton offense is beneficial to the survival of phytoplankton but may threaten the persistence of zooplankton population. An appropriate increase of phytoplankton defense or decrease of zooplankton offense can potentially change the survival state of the plankton system.