Dynamics of an autonomous Gilpin–Ayala competition model with random perturbation.

This paper discusses the dynamics of a Gilpin–Ayala competition model of two interacting species perturbed by white noise. We obtain the existence of a unique global positive solution of the system and the solution is bounded in p th moment. Then, we establish sufficient and necessary conditions for persistence and the existence of an ergodic stationary distribution of the model. We also establish sufficient conditions for extinction of the model. Moreover, numerical simulations are carried out for further support of present research. [ABSTRACT FROM AUTHOR]