Stationary distribution and ergodicity of a stochastic hybrid competition model with Lévy jumps

Taking white noises, Markovian switching and Lévy jumps into account, an n−species Lotka-Volterra competitive model with random perturbations is proposed and studied. Sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the model are established. These sufficient conditions are sharp in some cases. Some interesting results are revealed: the white noises and Lévy jumps could make the stationary distribution disappear as well as appear; the Markovian switching could make the stationary distribution appear. Some numerical simulations are also introduced to illustrate the main results.