Stochastic Lotka-Volterra systems under regime switching with jumps

Abstract

A stochastic Lotka-Volterra model with Markovian switching driven by jumps is proposed and
investigated. In the model, the white noise, color noise and the jumping noise are taken into account at the
same time. This model is more feasible and more applicable. First the sufficient conditions for stochastic
persistence and extinction are presented. Then the moment average in time and the asymptotic pathwise
properties are estimated. Our results show that these properties have close relations with the stationary
probability distribution of the Markov chain and the jumps. Finally, several simulation figures are provided
to illustrate the effectiveness of the results developed.