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Stochastically ultimate boundedness and global attraction of positive solution for a stochastic competitive system. (English) Zbl 1463.92051

Summary: A stochastic competitive system is investigated. We first show that the positive solution of the above system does not explode to infinity in a finite time, and the existence and uniqueness of positive solution are discussed. Later, sufficient conditions for the stochastically ultimate boundedness of positive solution are derived. Also, with the help of Lyapunov function, sufficient conditions for the global attraction of positive solution are established. Finally, numerical simulations are presented to justify our theoretical results.

MSC:

92D25 Population dynamics (general)
34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
34K20 Stability theory of functional-differential equations
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