Dynamics Analysis of a Stochastic Delay Gilpin-Ayala Model with Markovian Switching - Qiaoqin Gao; Zhijiang Luo; Guirong Liu (Discrete Dynamics in Nature and Society, 2019)
This paper considers a stochastic delay Gilpin-Ayala model with Markovian switching. Using Lyapunov method, we show existence and uniqueness of global positive solution. Then, by using Chebyshev’s inequality, M-matrix method, and BDG’s inequality, stochastic permanence and asymptotic estimations of solutions are studied. Finally, numerical simulations illustrate the theoretical results. Our results generalize and improve the existing results.