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Dynamical Behavior of a Stochastic Nutrient-Plankton Food Chain Model with L\'{e}vy Jumps
  
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KeyWord:Stochastic nutrient-plankton model, persistence and extinction, L$\acute{\rm e}$vy jumps
Author NameAffiliation
Zhenzhen Yang College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China 
Sanling Yuan College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China 
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Abstract:
      In aquatic ecosystem, plankton populations are easily affected by environmental fluctuations due to the unpredictability of many physical factors. To better understand how environmental fluctuations influence plankton populations, in this paper, we propose and investigate a stochastic nutrient-plankton food chain model with L$\acute{\rm e}$vy jumps. Firstly, by constructing a suitable Lyapunov function, we prove that the stochastic model has a unique global positive solution for any given positive initial value. Then, we establish sufficient conditions for the persistence and extinction of plankton. Finally, we provide some numerical simulations to illustrate the analytical results.