两种群随机捕食-食饵系统的有界性(英文)
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摘要
研究了一类两种群随机Lotka-Volterra捕食-食饵模型.在适当的环境噪音假设下,证明了此系统存在唯一正的全局解,并且这个解是随机最终有界的.
A class of two species stochastic Lotka-Volterra predator-prey system is discussed. We show that, under a suitable hypothesis on the environmental noise, the stochastic Lotka-Volterra system has a unique global positive solution and this positive solution will be stochastically ultimately bounded.
A class of two species stochastic Lotka-Volterra predator-prey system is discussed. We show that, under a suitable hypothesis on the environmental noise, the stochastic Lotka-Volterra system has a unique global positive solution and this positive solution will be stochastically ultimately bounded.
引文
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[7]Cheng S R.Stochastic population systems[J].Stoch Anal Appl,2009,27:854-874.
[8]Luo Q,Mao X.Stochastic population dynamics under regime switching[J].J Math Anal Appl,2007,334:69-84.
[9]Mao X.Stochastic Diferential Equations and Applications[M].Chichester:Horwood Publishing,1997.
[2]Rudnicki R,Pikor K.Influence of stochastic perturbation on prey-predator systems[J].Math Biosci,2007,206:108-119.
[3]Liu M,Wang K.Persistence,extinction and global asymptotical stability of a non-autonomous predator-prey model with random perturbation[J].Appl Math Modell,2012,36:5344–5353.
[4]Mao X,Marion G,Renshaw E.Environmental Brownian noise suppresses explosions in populations dynamics[J].Stochastic Process Appl,2002,97:95-110.
[5]Pang S,Deng F,Mao X.Asymptotic properties of stochastic population dynamics[J].Dyn Contin Discrete Impuls Syst Ser A Math Anal,2008,15:603-620.
[6]Zhu C,Yin G.On competitive Lotka-Volterra model in random environments[J].J Math Anal Appl,2009,357:154-170.
[7]Cheng S R.Stochastic population systems[J].Stoch Anal Appl,2009,27:854-874.
[8]Luo Q,Mao X.Stochastic population dynamics under regime switching[J].J Math Anal Appl,2007,334:69-84.
[9]Mao X.Stochastic Diferential Equations and Applications[M].Chichester:Horwood Publishing,1997.