Abstract
By applying the comparison theorem, Lyapunov functional, and almost periodic functional hull theory of the impulsive differential equations, this paper gives some new sufficient conditions for the uniform persistence, global asymptotical stability, and almost periodic solution to a nonautonomous Lotka-Volterra predator-prey dispersal system with impulsive effects. The main results of this paper extend some corresponding results obtained in recent years. The method used in this paper provides a possible method to study the uniform persistence, global asymptotical stability, and almost periodic solution of the models with impulsive perturbations in biological populations. MSC:34K14, 34K20, 34K45, 92D25.
Highlights
Because of the ecological effects of human activities and industry, more and more habitats are broken into patches and some of them are polluted
The predator-prey system has been extensively studied by many scholars, many excellent results were obtained concerned with the persistent property and positive periodic solution of the system; see [ – ] and the references cited therein
In Section, some new sufficient conditions are obtained for the existence, uniqueness, and global asymptotical stability of the positive almost periodic solution of system ( . )
Summary
Because of the ecological effects of human activities and industry, more and more habitats are broken into patches and some of them are polluted. Considering the effect of almost periodically varying environment is an important selective forces on systems in a fluctuating environment, Meng and Chen [ ] studied the case of combined effects: dispersion, time delays, almost periodicity of the environment They investigated the following general nonautonomous Lotka-Volterra. By using the comparison theorem and functional hull theory of almost periodic system, the authors [ ] obtained some sufficient conditions for the uniform persistence, global asymptotical stability, and almost periodic solution to system To the best of the authors’ knowledge, in the literature, there are few papers concerning the permanence, global asymptotical stability, and almost periodic solution to the Lotka-Volterra type predatorprey dispersal system with impulsive effects. In Section , some new sufficient conditions are obtained for the existence, uniqueness, and global asymptotical stability of the positive almost periodic solution of system
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