Permanence of species in nonautonomous discrete Lotka–Volterra competitive system with delays and feedback controls

Abstract

A nonautonomous N-species discrete Lotka-Volterra competitive system of difference equations with delays and feedback controls is considered. New sufficient conditions are obtained for the permanence of this discrete system. The results indicate that one can choose suitable controls to make the species coexistence in the long run. Moreover, we give some examples to illustrate the feasibility of our result which can be well suited for computational purposes.

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

“…Sufficient conditions on the coefficients are given to guarantee that all the species are permanent. It is shown that these conditions are weaker than those of Liao et al 2008. …”

“…It was shown that in [1] Liao et al considered system 1.4 where all coefficients r i n , c i n , d i n , a ij n , e i n , and b i n were assumed to satisfy conditions 1.9 .…”

Existence and global attractivity of periodic solution for a discrete prey–predator model with sex structure

“…At the same time, the existence of periodic solutions for periodic discrete population systems also has been studied by using coincidence degree theory. Among these periodic solutions results of periodic discrete systems obtained by using coincidence degree, only some results are obtained for discrete population systems [9][10][11][12][13][14]. Furthermore, in these papers, global attractivity of a positive periodic solution is not taken into consideration.…”

Positive periodic solutions of functional differential equations with impulse on time scales

“…In recent years, many authors have investigated the existence and nonexistence of periodic solutions for functional differential and difference equations (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]). In fact, most functional systems can be classified into two types, continuous or discrete.…”