Evolution of Lotka-Volterra predator-prey systems under telegraph noise - P. Auger; N. H. Du; N. T. Hieu (Mathematical Biosciences and Engineering)
In this paper we study a Lotka-Volterra predator-prey system with prey logisticgrowth under the telegraph noise. The telegraph noise switches at random two prey-predator models. The aim of this work is to determinethe subset of omega-limit set of the system and show out the existence of a stationarydistribution. We also focus on persistence of the predator and thus we look forconditions that allow persistence of the predator and prey community. We showthat the asymptotic behaviour highly depends on the value of some constant$λ$ which is useful to make suitable predictions aboutthe persistence of the system.