Permanence for multi-species nonautonomous Lotka-Volterra cooperative systems

Abstract

Abstract. In this paper, we establish sufficient conditions under which Lotka-Volterra cooperative systems are permanent for the n-dimensional case. We improve the result of [G. Lu and Z. Lu, Permanence for two species LotkaVolterra systems with delays, Math. Biosci. Engi. 5 (2008), 477-484] for the 2-dimensional case in that no restrictions of the size of time delays are needed. When the interval of time delays is constant, we further show that the restriction of the size of time delays is not required for the case n = 2, but it is required for the case n ≥ 3 to obtain lower bounds of solutions. An example is offered to illustrate the feasibility of our results