TY - JOUR AU - Li, Yanqing AU - Zhang, Long PY - 2017 TI - The stochastic interactions between predator and prey under Markovian switching: competitive interaction between multiple prey JO - Journal of Nonlinear Sciences and Applications SP - 5622--5645 VL - 10 IS - 11 AB - In this paper, a class of predator-prey model with prey competition is proposed, in which the interactions of predation between predator and prey are randomised and subsequently evaluated under Markovian switching. By constructing appropriate Lyapunov functions and applying various analytical methods, sufficient conditions for the existence of unique global positive solution, stochastic permanence and mean extinction are established. In the permanence case, we also estimate the superior and inferior limits of the sample path in a time-averaged Markov decision. 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