Convergent and divergent solutions of a discrete nonautonomous Lotka-Volterra model

Dynamics of a discrete Lotka-Volterra model

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...

Persistence and Global Stability in Discrete Models of Pure-delay Nonautonomous Lotka-Volterra Type

In this paper, for the above discrete system of pure-delay type, by improving the former work (2002, J. Math. Anal. Appl. 273, 492-511) which extended the averaged condition offered by S. Ahmad and A. C. Lazer (2000, Nonlinear Analysis 40, 37-49), we offer conditions of persistence, and considering a Lyapunov-like discrete function to the above discrete system, we establish sufficient condition...

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 NONAUTONOMOUS DISCRETE LOTKA–VOLTERRA n-SPECIES COMPETITIVE SYSTEMS WITH PURE-DELAYS AND FEEDBACK CONTROLS

The paper discusses nonautonomous discrete Lotka–Volterra type n-species competitive systems with pure-delays and feedback controls. New sufficient conditions for which a part of the n-species remains permanent and others is driven to extinction are established by using the method of multiple discrete Lyapunov functionals and introducing new analysis technique. Our results show that the feedbac...