Abstract
In this paper a class of cooperative Lotka-Volterra population system with time delay is considered. Some sufficient conditions on the existence and globally asymptotically stability for the asymptotically periodic solution of the system are established by using the Lyapunov function method and the method given in Fengying Wei and Wang Ke (Applied Mathematics and Computation 182 (2006) 161-165).
Highlights
Since Lotka-Volterra system has been established and was accepted by many scientists, it becomes the most important means to explain the ecological phenomenon
A lot of extensive research results were made in mathematical biology and mathematical ecology [1]-[8], during this time LotkaVolterra system has played an important role in theses research field of mathematical biology and mathematical ecology
From the viewpoint of mathematical biology, in this paper, for system (1) we consider the solution with the following initial condition x1 = (t ) φ1 (t ) ≥ 0, for t ∈[−2τ, 0] and φ1 (0) > 0, (2)
Summary
Since Lotka-Volterra system has been established and was accepted by many scientists, it becomes the most important means to explain the ecological phenomenon now. Lotka-Volterra Cooperative System, Asymptotically Periodic Function, Global Still many research work mostly discussed periodic Lotka-Volterra systems [2] [3] [4] [5] [6] and the references cited therein.
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