Impact of Plankton Body Size on a Stochastic Plankton System with Lévy Jumps (Journal of Nonlinear Modeling and Analysis, 2025)
In consideration of the important impact of plankton body sizeand Lévy noise on plankton system, a stochastic phytoplankton-zooplanktonsystem with Lévy jump is proposed and investigated in this paper. Firstly,we prove that there is a unique global positive solution to the system byusing Lyapunov function and ${\rm It}\check{o}$ formula. Then, some thresholds which depend on plankton body size are given, and they determine the extinction andweak persistence in the mean of plankton populations. In addition, the sufficient conditions for the existence of a stationary distribution of the solutionare given. Finally, some numerical simulations are introduced to support themain theoretical results and illustrate the impact of plankton body size andenvironmental noise on plankton populations.