Permanence for multi-species nonautonomous Lotka-Volterra cooperative systems

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 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...

Existence of multiple positive periodic solutions to n species nonautonomous Lotka - Volterra cooperative systems with harvesting terms

In this paper, the existence of 2 positive periodic solutions for n species non-autonomous Lotka-Volterra cooperative systems with harvesting terms is established by using Mawhin’s continuation theorem of coincidence degree theory and matrix inequality. An example is given to illustrate the effectiveness of our results. Keywords—Multiple positive periodic solutions; Nonautonomous Lotka-Volterra...

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...

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