带有Lévy跳与饱和项的随机互惠种群模型的渐近行为
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摘要
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 ■, 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.
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 ■, 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.
引文
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[4] 刘思润.一类随机互惠模型的渐近性质[D].哈尔滨:哈尔滨工业大学,2016.
[5] WEI T,WANG S,WANG L.Permanence and extinction of stochastic competitive Lotka–Volterra system with Lévy noise[J].Applied Mathematics and Computation,2018,57:667–683.
[6] LIU M,WANG K,WU Q.Survival Analysis of Stochastic Competitive Models in a Polluted Environment and Stochastic Competitive Exclusion Principle[J].Bulletin of Mathematical Biology,2011,73(9):1969-2012.
[7]杨金祥.具有时滞的双向联想记忆神经网络的稳定性分析[J].西南民族大学学报(自然科学版),2018,44(1):83-86.
[2] LUO Z,FAN X .Optimal control for an age-dependent competitive species model in a polluted environment[J].Applied Mathematics and Computation,2014,228(228):91-101.
[3] WANG X,JIA J .Dynamic of a delayed predator-prey model with birth pulse and impulsive harvesting in a polluted environment[J].Physica A Statistical Mechanics and its Applications,2015,422(422):1-15.
[4] 刘思润.一类随机互惠模型的渐近性质[D].哈尔滨:哈尔滨工业大学,2016.
[5] WEI T,WANG S,WANG L.Permanence and extinction of stochastic competitive Lotka–Volterra system with Lévy noise[J].Applied Mathematics and Computation,2018,57:667–683.
[6] LIU M,WANG K,WU Q.Survival Analysis of Stochastic Competitive Models in a Polluted Environment and Stochastic Competitive Exclusion Principle[J].Bulletin of Mathematical Biology,2011,73(9):1969-2012.
[7]杨金祥.具有时滞的双向联想记忆神经网络的稳定性分析[J].西南民族大学学报(自然科学版),2018,44(1):83-86.