Global attractivity and almost periodic solution of a discrete mutualism model with delays

Abstract

In this paper, we consider an almost periodic discrete Lotka–Volterra mutualism model with delays. We first obtain the permanence and global attractivity of the system. By means of an almost periodic functional hull theory and constructing a suitable Lyapunov function, sufficient conditions are obtained for the existence of a unique strictly positive almost periodic solution, which is globally attractive. An example together with numerical simulation indicates the feasibility of the main result. Copyright © 2013 John Wiley & Sons, Ltd.

Almost Periodic Solution of a Multispecies Discrete Mutualism System with Feedback Controls

“…Topics such as permanence, global attractivity, and global stability of continuous differential mutualism system were extensively investigated (see [2][3][4][5][6][7] and the references cited therein). In addition, some recent attention was on the permanence and global stability of discrete mutualism system, and many excellent results have been derived (see [3,[8][9][10][11][12][13] and the references cited therein).…”

“…Recently, the multispecies descrete Lotka-Volterra ecosystem is increasingly concerned (see [12][13][14][15][16][17][18][19][20][21] and the references cited therein). Yang and Li [19] studied a discrete nonlinear N-species cooperation system with time delays and feedback controls.…”

“…For this reason, the assumption of almost periodicity is more realistic, more important, and more general when we consider the effects of the environmental factors. In fact, there have been many nice works on the positive almost periodic solutions of continuous and discrete dynamics model with almost periodic coefficients (see [7,12,13,[22][23][24][25][26][27][28] and the references cited therein).…”

Global Analysis of Almost Periodic Solution of a Discrete Multispecies Mutualism System

“…A number of scholars have studied the difference system (see [1][2][3][4][5][6][7][8] and the references cited therein) since the discrete time models governed by the difference equation are more appropriate than the continuous ones when the populations have short life expectancy, nonoverlapping generations in the real world.…”

“…At the same time, a few scholars have investigated the mutualism system (see [2,[8][9][10][11][12][13] in detail). However, to the best of the authors' knowledge, still no scholar has done works on discrete multispecies mutualism system.…”