The threshold of stochastic Gilpin–Ayala model subject to general Lévy jumps

  • Chun Lu
  • Lijuan ChenEmail author
  • Yumin Wang
  • Shan Gao
Original Research


This paper investigates a stochastic Gilpin–Ayala model with general Lévy jumps and stochastic perturbation to around the positive equilibrium of corresponding deterministic model. Sufficient conditions for extinction are established as well as nonpersistence in the mean, weak persistence and stochastic permanence. The threshold between weak persistence and extinction is obtained. Asymptotic behavior around the positive equilibrium of corresponding deterministic model is discussed. Our results imply the general Lévy jumps is propitious to population survival when its intensity is more than 0, and some changes profoundly if not. Numerical simulink graphics are introduced to support the analytical findings.


Brownian motion General Lévy jumps Persistence Stability 

Mathematics Subject Classifications

60J65 60J60 34D20 



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Copyright information

© Korean Society for Computational and Applied Mathematics 2019

Authors and Affiliations

  1. 1.Department of MathematicsQingdao University of TechnologyQingdaoChina
  2. 2.Department of Mechinery and ElectricQingdao Technical CollegeQingdaoChina

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