Dynamics of a stochastic nutrient–plankton model with regime switching

Abstract

In this paper, a stochastic nutrient–plankton model with regime switching is proposed, where the regime switching plankton mortality is described by a continuous time Markov chain with different states. We study the effects of regime switching plankton mortality on the distribution of plankton biomass as well as the persistence and extinction of plankton populations. Moreover, we show that there exists a unique stationary distribution in the model, which is ergodic, indicating that the plankton populations will survive forever. By applying a sophisticated sensitivity analysis technique, we found that the phytoplankton biomass is highly sensitive to the grazing rate by zooplankton and least sensitive to the re-mineralization of dead biomass of plankton into nutrients concentration. The numerical results show that the persistence and extinction of plankton populations is sensitive to variations of nutrient input. We find that the noise can enhance the oscillations of plankton biomass and the regime switching plankton mortality has capacity to decrease the amplitudes of the oscillations in the bloom phase. Our findings emphasize that the regime switching plankton mortality contributes to the survival of plankton populations in the aquatic system.