Permanence and Almost Periodic Solutions of a Discrete Ratio-Dependent Leslie System with Time Delays and Feedback Controls

Abstract

We consider a discrete almost periodic ratio-dependent Leslie system with time delays and feedback controls. Sufficient conditions are obtained for the permanence and global attractivity of the system. Furthermore, by using an almost periodic functional Hull theory, we show that the almost periodic system has a unique globally attractive positive almost periodic solution.

Permanence for a Discrete Ratio-Dependent Predator-Prey System with Holling Type III Functional Response and Feedback Controls

“…Comparing with Theorem A, it is easy to see that ( ) in Theorem B are weaker than ( ) in Theorem A ( = 1, 2) and feedback control variables have no influence on the permanent property of system (1), so our results improve the main results in [1]. For more works on this direction, one could refer to [3][4][5][6][7][8][9][10] and the references cited therein.…”

Almost Periodic Positive Solution of a Discrete Delay Leslie Dynamics System with Feedback Controls

“…The proof of Proposition 2.1 is similar to that of Theorem 3.1 in Ref. [3] and Theorem 3.1 in Ref. [4].…”

“…As we all known, investigating the almost periodic positive solutions of discrete Leslie dynamics system has more extensively practical application value (see [1][2][3] and the references cited therein).In this paper, we investigate the dynamic behavior of the following discrete delay Leslie dynamics system with feedback controls ( ) ( 1) ( ) exp ( ) (…”

Analysis of Mathematics and Sustainability in an Impulsive Eutrophication Controlling System

“…In recent years, Fan et al [22] have proposed the dynamics of a class of mutualismcompetition-predator interaction models with Beddington-DeAngelis functional responses and impulsive perturbations; this work is important for solving the global stability and the globally exponential stability of system. Yu and Lu [23] mainly focused on the permanence and global attractivity of a discrete almost periodic ratio-dependent Leslie system with time delays and feedback controls; these works vigorously promote the application of feedback control. Shen et al [24] mainly have studied the permanence of a single species system with distributed time delay and feedback controls; it is a very important fact that the feedback control is harmless to the permanence of species; these works are significant for the application of feedback control in biological control.…”