TY - JOUR A2 - Eisencraft, Marcio AU - Wei, Chunjin AU - Fu, Yingjie PY - 2020 DA - 2020/01/20 TI - Stationary Distribution and Periodic Solution of Stochastic Toxin-Producing Phytoplankton–Zooplankton Systems SP - 4627571 VL - 2020 AB - In this paper, we investigate the dynamics of autonomous and nonautonomous stochastic toxin-producing phytoplankton–zooplankton system. For the autonomous system, we establish the sufficient conditions for the existence of the globally positive solution as well as the solution of population extinction and persistence in the mean. Furthermore, by constructing some suitable Lyapunov functions, we also prove that there exists a single stationary distribution which is ergodic, what is more important is that Lyapunov function does not depend on existence and stability of equilibrium. For the nonautonomous periodic system, we prove that there exists at least one nontrivial positive periodic solution according to the theory of Khasminskii. Finally, some numerical simulations are introduced to illustrate our theoretical results. The results show that weaker white noise and/or toxicity will strengthen the stability of system, while stronger white noise and/or toxicity will result in the extinction of one or two populations. SN - 1076-2787 UR - https://doi.org/10.1155/2020/4627571 DO - 10.1155/2020/4627571 JF - Complexity PB - Hindawi KW - ER -