Stochastic Population Systems

Abstract

Abstract In this article, we stochastically perturb the classical non-autonomous Lotka–Volterra model into the stochastic differential equation Different from most of existing articles, for example, [3 Bahar , A. , and Mao , X. 2004 . Stochastic delay population dynamics . International Journal of Pure and Applied Mathematics 11 : 377 – 400 . [Google Scholar], 20 Mao , X. 2005 . Delay population dynamics and environmental noise . Stochastics and Dynamics 5 ( 2 ): 149 – 162 .[Crossref], [Web of Science ®] , [Google Scholar]] the system parameters in this article are time-dependent. We will give a sufficient condition under which the stochastic differential equation will have a unique global positive solution. We will then establish some new asymptotic properties for the moments as well as for the sample paths of the solution. In particular, we will discuss two fundamental problems in population systems, namely ultimate boundedness and extinction.