Abstract
In this paper, we consider the almost periodic dynamics of a multispecies Lotka-Volterra mutualism system with time varying delays on time scales. By establishing some dynamic inequalities on time scales, a permanence result for the model is obtained. Furthermore, by means of the almost periodic functional hull theory on time scales and Lyapunov functional, some criteria are obtained for the existence, uniqueness and global attractivity of almost periodic solutions of the model. Our results complement and extend some scientific work in recent years. Finally, an example is given to illustrate the main results.
Highlights
There have been many scholars concerned with the dynamics of the mutualism model
Global attractivity, and periodicity of mutualism systems governed by differential equations were extensively investigated
In [ ], the author studied the existence of positive periodic solutions of the periodic mutualism model dx (t ) dt
Summary
There have been many scholars concerned with the dynamics of the mutualism model. By means of the theory of difference inequality and Lyapunov function, they established sufficient conditions for the existence and uniformly asymptotic stability of a unique positive almost periodic solution to system It is worthwhile continuing to study the existence and stability of a unique almost periodic solution of the multispecies Lotka-Volterra mutualism system with time varying delays. ) and, by using the almost periodic functional hull theory on time scales, to establish criteria for the existence and uniqueness of globally attractive almost periodic solutions of system In Section , some sufficient conditions are obtained for the existence of positive almost periodic solutions of system
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