Study On The Almost Periodic Solution To Ecological Systems

This paper is comprised of three parts:Firstly, a discrete mutualism model with infinite delays and feedback controls isinvestigated. We obtain sufficient conditions which guarantee the permanence of themodel by using the difference theorem.Secondly, almost periodic solutions to an almost periodic two-prey one-predatordiscrete model with Holling type II functional response is studied. By using twocomparison principles and analysis, some sufficient conditions are derived for thepersistence, then constructing a suitable Lyapunov function, we derive somesufficient conditions on the global stability of an unique almost periodic solution ofthe system.Finally, we investigate the following almost periodic discrete system withfeedback controls which describes the effect of toxic substances and age structuressimultaneously. By using two comparison principles and calculation, we obtain somesufficient conditions of the uniform persistence, and constructing a suitableLyapunov function, which satisfies the conditions of lemma in [1], some sufficientconditions are established on the uniqueness of positive almost periodic solution.