Stochastic Lotka-Volterra system with infinite delay

Authors:
Yong Xu;Fuke Wu;Yimin Tan
Affiliations:
School of Sciences, Central South University of Forestry and Technology, Changsha, Hunan, 410004, PR China and Department of Mathematics, Huazhong University of Science and Technology, Wuhan, Hube ...;Department of Mathematics, Huazhong University of Science and Technology, Wuhan, Hubei, 430074, PR China;Research Center of Forest Tourism, Central South University of Forestry and Technology, Changsha, Hunan, 410004, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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Abstract

This paper investigates a stochastic Lotka-Volterra system with infinite delay, whose initial data comes from an admissible Banach space C"r. We show that, under a simple hypothesis on the environmental noise, the stochastic Lotka-Volterra system with infinite delay has a unique global positive solution, and this positive solution will be asymptotic bounded. The asymptotic pathwise of the solution is also estimated by the exponential martingale inequality. Finally, two examples with their numerical simulations are provided to illustrate our result.