SUFFICIENT AND NECESSARY CONDITIONS FOR PERSISTENCE AND EXTINCTION OF A STOCHASTIC TWO-PREY ONE-PREDATOR SYSTEM

This paper applies a new approach for stochastic Kolmogorov systems generalized by Hening and Nguyen to describe the dynamics of a stochastic two independent prey one predator system perturbed by white noise. Through calculating Lyapunov exponents, we thoroughly address the stability of the ergodic invariant probability measures. Sufficient and necessary conditions under which the species persist as well as conditions under which some species go extinct are established for this three dimensional models. One of the key points is that the critical cases for Lyapunov exponents being zero are considered. Finally, some numerical simulations illustrate the analytical results.