Dynamics of Gilpin-Ayala competition model with random perturbation

Abstract

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 the stochastic Gilpin-Ayala competition model.

Asymptotic behavior of a stochastic Gilpin–Ayala predator–prey system with time-dependent delay

“…the i-th population (prey species) will become extinct exponentially with probability one. Moreover, if (27) holds for every i = 1, . .…”

“…Taking a stochastic approach to the problem assumes a more realistic look at how these populations interact. There are many papers which consider stochastic population models, mainly Lotka-Volterra models [19][20][21][22][23][24], but also several papers deal with stochastic Gilpin-Ayala competition systems [25][26][27][28]. However, to the best of the author's knowledge, up to now, there is no paper about the stochastic Gilpin-Ayala predator-prey model.…”

Caratheodory's approximate solution to stochastic differential delay equation

“…n } stands for the Lebesgue measure on R. For some more details on stochastic differential equations, refer to [1][2][3][5][6][7][8][9][10][11] and references therein. By using the nonlinear growth condition and nonlinear growth condition, in 2015, Kim [4] studied the difference between the approximate solution and the accurate solution to the stochastic differential delay equation (shortly, SDEs).…”

Global exponential stability of multi-group models with multiple dispersal and stochastic perturbation based on graph-theoretic approach

“…In the real world, stochastic perturbation exists everywhere, which has been mentioned in [16][17][18][19]. In addition, a system could be stable or unstable in response to stochastic perturbation.…”