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New results on the stochastic Gilpin-Ayala model with delays

Wang Kai (Anhui University of Finance and Economics, School of Statistics and Applied Mathematics, Bengbu, P.R. China)
Zhu Yanling (School of International Trade and Economics, University of International Business and Economics, Beijing, P.R. China)
Zhu Hailong (Anhui University of Finance and Economics, School of Statistics and Applied Mathematics, Bengbu, P.R. China)

In this paper, a stochastic Gilpin-Ayala model with delays is investigated. Some new sufficient conditions for the existence of positive and global solution of the model are obtained. Moreover, asymptotic behavior of the model is discussed. It is significant that these results improve the previous work (Lian and Hu, Stochastic delay Gilpin-Ayala competition models, Stochastic Dynamics 6 (2006) 561-576).

Keywords: stochastic differential equation, brownian motion, moment boundedness, asymptotic behavior