Abstract
This article presents an investigation of asymptotic properties of a stochastic ratio-dependent predator-prey model under regime switching. Both the white and color noises are taken into account in our model. We obtain the global existence of positive unique solution of the stochastic model. And we show the solution is bounded in mean. Moreover, the sufficient conditions for persistence in mean, extinction are obtained.
Highlights
The dynamic interaction between the predators and their prey has long been one of the dominant themes in mathematical biology because of its universal existence and importance
As a matter of fact, population systems is often subject to environmental noise
Stochastic differential equation under regime switching Throughout this article, unless otherwise specified, we let (, F .{Ft}t≥0,P) be a complete probability space with a filtration {Ft}t≥0 satisfying the usual conditions
Summary
The dynamic interaction between the predators and their prey has long been one of the dominant themes in mathematical biology because of its universal existence and importance. Where Bi(t), i = 1, 2, are independent standard Brownian motions 2. Stochastic differential equation under regime switching Throughout this article, unless otherwise specified, we let ( , F .{Ft}t≥0,P) be a complete probability space with a filtration {Ft}t≥0 satisfying the usual conditions (i.e., it is right continuous and F0 contains all P-null sets.).
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