Global Attractivity and Extinction of a Discrete Competitive System with Infinite Delays and Single Feedback Control

Abstract

A nonautonomous discrete two-species competition system with infinite delays and single feedback control is considered in this paper. Based on the discrete comparison theorem, a set of sufficient conditions which guarantee the permanence of the system is obtained. Then, by constructing some suitable discrete Lyapunov functionals, some sufficient conditions for the global attractivity and extinction of the system are obtained. It is shown that, by choosing some suitable feedback control variable, one of two species will be driven to extinction.

Dynamic behaviors of a Lotka-Volterra type predator-prey system with Allee effect on the predator species and density dependent birth rate on the prey species

“…During the last decades, many scholars [2][3][4][5][6][22][23][24][25] investigated the in uence of Allee e ect on the dynamic behaviors of ecosystem. Also, there are several scholars [32][33][34][35][36][37][38] investigated the almost periodic solution of the ecosystem. However, all of those studies are based on the traditional Logistic model.…”

“…It is well known that in a more realistic model the delay e ect should be an average over past populations. This results in an equation with a distributed delay or an in nite delay [29][30][31][32][33][34][35][36][37][38][39][40][41]. Here, if we incorporate the in nite delay to system (1.6), then we will have the following system…”

Almost periodic solution of a discrete competitive system with delays and feedback controls

“…( ) Besides, Gopalsamy [2] discussed the continuous version with discrete delays, Tan and Liao [3] established the discrete time version with discrete delays, Xue et al [4] proposed the discrete time version with in nite delays and single feedback control. Recently, the almost periodic solutions of discrete system with feedback controls has more extensively investigated (see [5][6][7][8][9][10]).…”

Dynamic behaviors of a stage-structured commensalism system

“…On the other hand, many scholars investigated the dynamic behaviors of the stagestructured species, see [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45], and the references cited therein. In constructing a stagestructured model, two different ideas were applied.…”

“…(1.8) They showed that system (1.8) admits a unique positive equilibrium which is globally asymptotically stable. Many scholars [26][27][28][29][30][31][32][33][34][35][36][37][38][39] used the idea of Aiello and Freedman to establish stage-structured ecological models. For example, Chen et al [28] studied the persistence property of the following stage-structured predator-prey model:…”