Extinction and permanence in nonautonomous competitive system with stage structure

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...

Extinction in Nonautonomous Competitive Lotka-volterra Systems

It is well known that for the two species autonomous competitive Lotka-Volterra model with no fixed point in the open positive quadrant, one of the species is driven to extinction, whilst the other population stabilises at its own carrying capacity. In this paper we prove a generalisation of this result to nonautonomous systems of arbitrary finite dimension. That is, for the n species nonautono...

Permanence and extinction for a nonautonomous SEIRS epidemic model

In this paper, we study the long-time behavior of a nonautonomous SEIRS epidemic model. We obtain new su cient conditions for the permanence (uniform persistence) and extinction of infectious population of the model. By numerical examples we show that there are cases such that our results improve the previous results obtained in [T. Zhang and Z. Teng, On a nonautonomous SEIRS model in epidemiol...

Extinction in Nonautonomous Discrete Lotka-Volterra Competitive System with Pure Delays and Feedback Controls

The coexistence and global stability of population models are of the interesting subjects in mathematical biology. Many authors have argued that the discrete time models are governed by differential equations which are more appropriate than the continuous ones to describe the dynamics of population when the population has nonoverlapping generations, a lot has been done on discrete Lotka-Volterr...

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