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| Impact of Plankton Body Size on a Stochastic Plankton System with L$\acute{e}$vy Jumps |
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| KeyWord:Phytoplankton-zooplankton system, L$\acute{e}$vy jump, Lyapunov function, It$\check{o}$ formula, stationary distribution |
| Author Name | Affiliation | | Shulin Sun | School of Mathematics and Computer Science, Shanxi Normal University, Taiyu Road 339, 030031, Taiyuan, China | | Yaping Jin | School of Mathematics and Computer Science, Shanxi Normal University, Taiyu Road 339, 030031, Taiyuan, China | | Cuihua Guo | School of Mathematics Science, Shanxi University, Wucheng Road 92, 030006, Taiyuan, China |
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| Abstract: |
| In consideration of the important impact of plankton body size and L$\acute{e}$vy noise on plankton system, a stochastic phytoplankton-zooplankton system with L$\acute{e}$vy jump is proposed and investigated in this paper. Firstly, we prove that there is a unique global positive solution to the system by using Lyapunov function and It$\check{o}$ formula. Then, some thresholds which depend on plankton body size are given, and they determine the extinction and weak persistence in the mean of plankton populations. In addition, the sufficient conditions for the existence of a stationary distribution of the solution are given. Finally, some numerical simulations are introduced to support the main theoretical results and illustrate the impact of plankton body size and environmental noise on plankton populations. |
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