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Discrete Dynamics in Nature and Society
Volume 2019, Article ID 1302648, 15 pages
Research Article

Dynamics Analysis of a Stochastic Delay Gilpin-Ayala Model with Markovian Switching

1Department of Mathematics, Luliang University, Lishi, Shanxi 033001, China
2School of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi 030006, China

Correspondence should be addressed to Guirong Liu; nc.ude.uxs@1975rgl

Received 1 February 2019; Accepted 16 May 2019; Published 4 June 2019

Academic Editor: Giancarlo Consolo

Copyright © 2019 Qiaoqin Gao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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, -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.