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Dynamical analysis of a stochastic predator-prey model with an Allee effect. (English) Zbl 1288.92029

Summary: We present and analyze a modified Holling type-II predator-prey model that includes some important factors such as Allee effects, density-dependence, and environmental noise. By constructing suitable Lyapunov functions and applying the Itô formula, some qualitative properties are given, such as the existence of global positive solutions, stochastic boundedness, and the global asymptotic stability. A series of numerical simulations to illustrate these mathematical findings are presented.

MSC:

92D40 Ecology
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)

References:

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