Hybrid competitive Lotka–Volterra ecosystems with a hidden Markov chain

查看全文 作　　者：Ky [1]Tran;George [1]Yin

机构地区：[1]Department of Mathematics,Wayne State University,Detroit,MI,USA

出　　处：《Journal of Control and Decision》索引2014年第1卷第1期,共24页

基　　金：This work was supported in part by the National Science Foundation under DMS-1207667. 摘　　要：This work concerns Lotka–Volterra models that are formulated using stochastic differential equations with regime-switching.Distinct from the existing formulations,the Markov chain that models random environments is unobservable.For such partially observed systems,we use Wonham’s filter to estimate the Markov chain from the observable evolution of the population,and convert the original system to a completely observable one.We then show that the positive solution of our model does not explode in finite time with probability 1.Several properties including stochastic boundedness,finite moments,sample path continuity and large-time asymptotic behaviour are also obtained.Moreover,stochastic permanence,extinction and feedback controls are also investigated. 关键词：Lotka-Volterra model hidden Markov chain partially observed system

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Hybrid competitive Lotka–Volterra ecosystems with a hidden Markov chain

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