Dynamics of stochastic Gilpin-Ayala model with finite Markov chain and Lévy jumps driven by mean-reverting OU process
A stochastic Gilpin-Ayala model with finite Markov chain and Lévy jumps driven by mean-reverting OU(Ornstein-Uhlenbeck)process was proposed and asymptotic behaviors of the stochastic Gilpin-Ayala model were studied.Firstly,the existence of the global solution of the stochastic Gilpin-Ayala population model was proved by selecting an appropriate Lyapunov function.Secondly,the moment boundedness of the solution to the stochastic Gilpin-Ayala population model was given.Then the existence of a stationary distribution of solutions for the stochastic Gilpin-Ayala population model was proved.Finally,the extinction of the stochastic Gilpin-Ayala population model was proved.The theoretical results were verified through numerical examples and numerical simulations.
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