Periodic solutions of a discrete nonautonomous Lotka-Volterra predator-prey model with time delays

A Delay Almost Periodic Competitive System in Discrete Time

“…Moreover, if there exists a solution ( ) of system (7) such that ‖ ‖ ≤ * ≤ for all ∈ + , then there exists a unique uniformly asymptotically stable almost periodic solution ( ) of system (7) which satisfies | ( )| ≤ * for all ∈ . In particular, if ( , ) is periodic of period , then system (7) has a unique uniformly asymptotically stable periodic solution of period .…”

“…As we know, a discrete time model governed by difference equations is more suitable than a corresponding continuous version when the populations have a short-life expectancy and nonoverlapping generations and can also provide efficient computation for numerical simulation (see [1][2][3][4][5][6][7]). On the other hand, the coefficients of model are changed owing to environmental variation.…”

Permanence and Positive Periodic Solutions of a Discrete Delay Competitive System

“…Therefore, the dynamic behaviors of population models governed by difference equations have been studied by many authors, see 12-18 and the references cited therein. Noting that some studies of the dynamics of natural populations indicate that the density-dependent population regulation probably takes place over many generations 19, 20 , many authors have discussed the influence of many past generations on the density of species population and discussed the dynamic behaviors of competitive, predator-prey, and cooperative systems see 21-24 . Motivated by the above work [19][20][21][22][23][24] , in this paper we will investigate the following discrete time non-autonomous two-species competitive system with delays:…”

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

“…Similar models have been studied by many people. For example, Wang et al in [6] studied the global stability of discrete population models, Xu et al in [7] investigated a discrete periodic two-species Lotka-Volterra predator-prey model with time delays by using Gaines and Mawhin's continuation theorem of coincidence degree theory, and Li and Ratfoul in [8] studied a classification scheme for the eventually positive solutions of a class of two-dimensional Volterra nonlinear difference equations. Motivated by these and other works [1][2][3][4][5][6][7][8][9][10][11][12][13], in the present paper, we discuss the existence of certain solutions of system (1).…”