The impact of temperature variation on the algae–zooplankton dynamics with size-selective disturbance

Abstract

The phenomenon of algal blooms caused by global warming frequently occurs in global water bodies, however, the mechanism by which temperature affects algal growth is still unclear. In this paper, we investigate the dynamics of a deterministic algae–zooplankton model with water temperature, as well as its corresponding stochastic version. Mathematical theoretical work mainly analyzes the stability, persistence and Hopf bifurcation of the deterministic model, and performs a survival analysis on the stochastic model and shows the existence of a unique ergodic stationary distribution, which in turn provides a theoretical basis for numerical simulations. Numerical analysis indicates that the variation of temperature can generate complex impacts on the fundamental mechanisms underlying the growth of algae, whether in deterministic or stochastic environment. One of the most interesting results indicates that the decrease of temperature can destabilize the algae–zooplankton interactions, but increase their permanence; the increase of temperature can stabilize the algae–zooplankton interactions, but reduce their permanence.