带有Lévy跳与饱和项的随机互惠种群模型的渐近行为

Asymptotic properties of a stochastic mutualism model with a saturation term and Lévy jumps

考虑一类带有Lévy跳与饱和项的随机互惠种群模型.通过构造合适的Lyapunov函数,证明了该模型全局正解的存在唯一性.利用It■公式以及Lyapunov函数方法,给出2种群的灭绝性条件.当该模型不考虑Lévy跳的影响时,结果与已有文献的相应结果一致.从而,推广了已有文献的结果.最后,通过数值仿真验证了结果的合理性.

This paper investigates a stochastic mutualism model with a saturation term and Lévy jumps. It chooses a suitable Lyapunov function to demonstrate the existence and uniqueness of global positive solutions. Using It o ^ formula, the sufficient conditions for the extinction of each species are established. The results in this paper extend the results of the existing literature. Finally, some numerical simulations are given to illustrate the theoretical results.