Permanence of nonautonomous Lotka–Volterra delay differential systems

Permanence for multi-species nonautonomous Lotka-Volterra cooperative systems

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 tim...

Permanence and extinction for a nonautonomous SVIR epidemic model with distributed time delay∗

In this paper we have considered a nonautonomous SV IR epidemic model with varying total population size and distributed time delay to become infectious. Instead of assuming that vaccinees gain immunity immediately, we have assumed that they are different from susceptible and recovered persons and it takes some time for them to gain immunity and then enter into the recovered class. Here, we hav...

Qualitative Analysis of a Nonautonomous Nonlinear Delay Differential Equation

This paper is devoted to the systematic study of some qualitative properties of solutions of a nonautonomous nonlinear delay equation, which can be utilized to model single population growths. Various results on the boundedness and oscillatory behavior of solutions are presented. A detailed analysis of the global existence of periodic solutions for the corresponding autonomous nonlinear delay e...

Partial Extinction, Permanence, and Global Attractivity in Nonautonomous n-Species Gilpin-Ayala Competitive Systems with Impulses

In 1 , the general nonautonomous n-species Lotka-Volterra competitive systems with impulsive effects are investigated. By using the methods of inequalities estimate and constructing the suitable Liapunov functions, the sufficient conditions on the permanence of whole species and global attractivity of systems are established. In 2 , the authors studied the following general nonautonomous n-spec...

Permanence in Multispecies Nonautonomous Lotka-Volterra Competitive Systems with Delays and Impulses