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

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.

Existence of positive periodic solutions for the impulsive Lotka–Volterra cooperative population model with time-delay and harvesting control on time scales

“…Fortunately, the theory of calculus on time scales (see [21,22] and references therein) proposed by Hilger in his Ph.D. thesis [23] can unify continuous and discrete analysis, and it has become an effective approach to the study of mathematical models involving hybrid discrete-continuous processes. There are many achievements in the study of hybrid discrete-continuous mathematical models (see [24][25][26][27][28][29][30][31][32]). …”