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

Abstract

This paper discusses a discrete multispecies Lotka-Volterra mutualism system. We first obtain the permanence of the system. Assuming that the coefficients in the system are almost periodic sequences, we obtain the sufficient conditions for the existence of a unique almost periodic solution which is globally attractive. In particular, for the discrete two-species Lotka-Volterra mutualism system, the sufficient conditions for the existence of a unique uniformly asymptotically stable almost periodic solution are obtained. An example together with numerical simulation indicates the feasibility of the main result.

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).…”

Permanence and almost periodic solution of a multispecies Lotka-Volterra mutualism system with time varying delays on time scales

“…In recent years, the almost periodic solution of the models in biological populations has been studied extensively (see [11][12][13][14][15][16][17][18] 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 [19][20][21][22][23][24]). In [24], the authors considered the following discrete multispecies Lotka-Volterra mutualism system:…”

“…In addition, some recent attention was on the permanence and global stability of discrete mutualism system, and many excellent results have been derived (see [19][20][21][22][23][24]). In [24], the authors considered the following discrete multispecies Lotka-Volterra mutualism system:…”