Asymptotic behavior of non-autonomous stochastic Gilpin-Ayala predator-prey model with jumps
نویسنده
چکیده
In this paper, a non-autonomous stochastic Gilpin-Ayala predator-prey model with jumps is studied. Firstly, we show that this model has a unique global positive solution under certain conditions. Then, we discuss the sufficient conditions for stochastically ultimate boundedness and obtain the asymptotic behavior of the solution. Finally, sufficient criteria for extinction of all prey and predator species, stochastic weak persistence in the mean of prey species are established. c ©2017 All rights reserved.
منابع مشابه
Asymptotic Behavior of Stochastic Gilpin-ayala Mutualism Model with Jumps
This article concerns the study of stochastic Gilpin-Ayala mutualism models with white noise and Poisson jumps. Firstly, an explicit solution for one-dimensional Gilpin-Ayala mutualism model with jumps is obtained and the asymptotic pathwise behavior is analyzed. Then, sufficient conditions for the existence of global positive solutions, stochastically ultimate boundedness and stochastic perman...
متن کاملA non-autonomous stochastic predator-prey model.
The aim of this paper is to consider a non-autonomous predator-prey-like system, with a Gompertz growth law for the prey. By introducing random variations in both prey birth and predator death rates, a stochastic model for the predator-prey-like system in a random environment is proposed and investigated. The corresponding Fokker-Planck equation is solved to obtain the joint probability density...
متن کاملPermanence and global asymptotic stability of a delayed predator-prey model with Hassell-Varley type functional response
Here, a predator-prey model with Hassell-Varley type functional responses is studied. Some sufficient conditions are obtained for the permanence and global asymptotic stability of the system by using comparison theorem and constructing a suitable Lyapunov functional. Moreover, an example is illustrated to verify the results by simulation.
متن کاملDynamics of Gilpin-ayala Competition Model with Random Perturbation
In this paper we study the Gilpin-Ayala competition system with random perturbation which is more general and more realistic than the classical LotkaVolterra competition model. We verify that the positive solution of the system does not explode in a finite time. Furthermore, it is stochastically ultimately bounded and continuous a.s. We also obtain certain results about asymptotic behavior of t...
متن کاملStochastic functional population dynamics with jumps
In this paper we use a class of stochastic functional Kolmogorov-type model with jumps to describe the evolutions of population dynamics. By constructing a special Lyapunov function, we show that the stochastic functional differential equation associated with our model admits a unique global solution in the positive orthant, and, by the exponential martingale inequality with jumps, we dis...
متن کامل