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

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...

Partial Survival and Extinction of Species in Nonautonomous Lotka-Volterra Systems with Delays

This paper concerns with the principle of competitive exclusion which is extended by Shair Ahmad (1999, Proceedings of the American Mathematical Society 127, 29052910), that is, if the coefficients satisfy certain inequalities, then any solution with positive components at some point will have all of its last n − 1 components tend to zero, while the first one will stabilize at a certain solutio...

Note on the Persistent Property of a Discrete Lotka-Volterra Competitive System with Delays and Feedback Controls

Global Stability of a Autonomous Stochastic Lotka-Volterra Competitive System with Feedback Controls and Infinite Delays

In this paper, we consider an autonomous Lotka-Volterra stochastic competitive system with feedback controls and infinite delays. Sufficient conditions which ensure the global stability of the system is considered. Some simulation figures are introduced to support the analytical findings.

Persistence and Extinction for General Nonautonomous n-Species Lotka–Volterra Cooperative Systems with Delays

The general nonautonomous n-species Lotka–Volterra cooperative systems with varying-time delays are studied. Sufficient conditions for the uniform strong persistence, uniform weak average persistence, uniform strong average persistence, and extinction of populations are obtained by applying the method of Liapunov functionals. Particularly, when the intrinsic growth rate of a species is nonposit...