Threshold behavior in a stochastic algal growth model with stoichiometric constraints and seasonal variation

Abstract

In this paper, we propose and investigate a stochastic algal growth model with the explicit incorporation of season-dependent light and nutrient availability. We first establish the threshold 〈λ〉ϖ that determines the persistence and extinction of the algae: when 〈λ〉ϖ>0, the algal will persist in mean, while when 〈λ〉ϖ<0, the algae will eventually die out. Then we prove the existence and global attractiveness of a positive stochastic periodic solution when 〈λ〉ϖ>0 by constructing suitable Lyapunov functions. Numerical simulations are carried out to substantiate our analytical results and investigate effective methods to control algal blooms.