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Abstract: This paper discusses a randomized n-species Lotka–Volterra competition system. We show that this system is stable in time average under certain conditions. Furthermore, there is a stationary distribution of this system, if extra conditions are satisfied. Also we give the extinction condition of this system. Finally, numerical simulations are carried out to support our results. [Copyright &y& Elsevier]

Abstract: In this paper, we discuss a stochastic density dependent predator–prey system with Beddington–DeAngelis functional response. First, we show that this system has a unique positive solution as this is essential in any population dynamics model. Then, we investigate the asymptotic behavior of this system. When the white noise is small, the stochastic system imitates the corresponding deterministic system. Either there is a stationary distribution, or the predator population will die out. While if the white noise is large, besides the extinction of the predator population, both species in the system may also die out, which does not happen in the deterministic system. Finally, simulations are carried out to conform to our results. [Copyright &y& Elsevier]

Abstract: In this paper, we show there is a stationary distribution of a predator–prey model with modified Leslie–Gower and Holling-type II schemes with stochastic perturbation and it has ergodic property. [ABSTRACT FROM AUTHOR]