In the real world, the population systems are often subject to white noises and a system with such stochastic perturbations tends to be suitably modeled by stochastic differential equations. This paper is concerned with the dynamic behaviors of a delay stochastic competitive system. We first obtain the global existence of a unique positive solution of system. Later, we show that the solution of system will be stochastically ultimate boundedness. However, large noises may make the system extinct exponentially with probability one. Also, sufficient conditions for the global attractivity of system are established. FinMly, illustrated examples are given to show the effectiveness of the proposed criteria.
In this paper, a nonautonomous stochastic food-chain system with functional response and impulsive perturbations is studied. By using Ito＇s formula, exponential martingale inequality, differential inequality and other mathematical skills, some sufficient conditions for the extinction, nonpersistence in the mean, persistence in the mean, and stochastic permanence of the system are established. Furthermore, some asymptotic properties of the solutions are also investigated. Finally, a series of numerical examples are presented to support the theoretical results, and effects of different intensities of white noises perturbations and impulsive effects are discussed by the simu｜ations.
In this paper,a novel stochastic two-species competitive system with saturation effect is formulated,in which there exist two noise resources and their coupling mode is relatively complex and every noise source has elfect on the intrinsic growth rates of both species.With the help of some suitable Lyapunov functions,sufficient conditions for stochastic permanence are established as exponential extinction,extinction,permanence in time average and asymptotic pathwise estimation of system.The effect of coupling noise on the asymptotic behaviors of the populations is shown.
