带Lévy跳的随机互惠模型持久性
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摘要
针对一类带Lévy跳的随机互惠模型,通过构造Lyapunov函数证明了模型全局正解的存在唯一性;然后,应用It公式与Chebyshev不等式得到该模型随机持久的充分条件;最后,通过数值模拟验证了理论结果的合理性。研究结果表明:较小的Lévy噪声不会破坏种群的持续生存。
For a class of stochastic mutualism model with Lévy jumps,the existence and uniqueness of the global positive solution of the model was proved by constructing Lyapunov function. Then,by using the It8's formula and the Chebyshev's inequality,the sufficient condition for the stochastic permanence of the model was obtained. Finally,the rationality of the theoretical results was verified by numerical simulation. The research results show that small Lévy jumps can not disrupt the permanence of the population.
For a class of stochastic mutualism model with Lévy jumps,the existence and uniqueness of the global positive solution of the model was proved by constructing Lyapunov function. Then,by using the It8's formula and the Chebyshev's inequality,the sufficient condition for the stochastic permanence of the model was obtained. Finally,the rationality of the theoretical results was verified by numerical simulation. The research results show that small Lévy jumps can not disrupt the permanence of the population.
引文
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[2]聂文静,王辉,胡志兴,等.一类具有时滞和随机项的捕食-被捕食模型[J].河南科技大学学报(自然科学版),2015,36(6):75-81.
[3]ZHU Y,LIU M.Permanence and extinction in a stochastic service-resource mutualism model[J].Applied mathematics letters,2017,69:1-7.
[4]LIU Q,CHEN Q,HU Y.Analysis of a stochastic mutualism model[J].Communications in nonlinear science and numerical simulation,2015,29(1/3):188-197.
[5]HE X,SHAN M,LIU M.Persistence and extinction of an n-species mutualism model with random perturbations in a polluted environment[J].Physica a(statistical mechanics and its applications),2018,491:313-324.
[6]XU C,YUAN S,ZHANG T.Sensitivity analysis and feedback control of noise-induced extinction for competition chemostat model with mutualism[J].Physica a(statistical mechanics and its applications),2018,505:891-902.
[7]LI M,GAO H,WANG B.Analysis of a non-autonomous mutualism model driven by Lévy jumps[J].Discrete and continuous dynamical systems-series b,2015,21(4):1189-1202.
[8]GUO S L,HU Y J.Asymptotic behavior and numerical simulations of a Lotka-Volterra mutualism system with white noises[J].Advances in difference equations,2017,2017(1):125.
[9]LIU Q,JIANG D,SHI N,et al.Stochastic mutualism model with Lévy jumps[J].Communications in nonlinear science and numerical simulation,2017,43:78-90.
[10]ZHANG Q,JIANG D,ZHAO Y,et al.Asymptotic behavior of a stochastic population model with Allee effect by Lévy jumps[J].Nonlinear analysis hybrid systems,2017,24:1-12.
[11]QIU H,DENG W.Optimal harvesting of a stochastic delay competitive Lotka-Volterra model with Lévy jumps[J].Applied mathematics and computation,2018,317:210-222.
[12]YU J,LIU M.Stationary distribution and ergodicity of a stochastic food-chain model with Lévy jumps[J].Physica a(statistical mechanics and its applications),2017,482:14-28.
[13]WANG S,WANG L,WEI T.Permanence and asymptotic behaviors of stochastic predator-prey system with Markovian switching and Lévy noise[J].Physica a(statistical mechanics and its applications),2018,495:294-311.
[14]APPLEBAUM D.Lévy processes and stochastic calculus[M].Cambridge:Cambridge University Press,2009.
[15]MAO X.Stochastic differential equations and applications[M].Chichester:Horwood Publishing Limited,2007.