The Study Of The Existence Of Positive Periodic Solution For Some Cooperative Systems

Mathematical ecological dynamic system has already become one of the hotspot of the study of modern mathematical biology. It's dynamical behavior includes extinction, permanence, local or global stability, the existence of periodic solution, almost periodic solution, asymptotic periodic solution and the oscillation of solution and so on and so forth. Therein, the existence of periodic solution has already become one of the most interested subjects for researchers no matter in home and abroad. In this paper, we study the existence of positive periodic solution for some population dynamical cooperative systems by using continuation theorem of degree theory.The main contents in this paper can be summarized as follows:1. in section 1, we introduce the biological background and significance of this paper. Then, we introduced some study result for some cooperative systems and the model of what we will study in this paper. Finally, we present some definitions and lemmas which is useful for our main results in this paper.2. from section 2, we had study n-species Lotka-Volterra cooperative system with distributed delays and via employing continuation theorem of the coincidence degree the-ory developed by Gaines and Mawhin to established sufficient conditions for the existence of positive periodic solutions.3. from section 3, we had study two-species Lotka-Volterra cooperative system with distributed delays and nonlinear diffusions and via employing continuation theorem of the coincidence degree theory developed by Gaines and Mawhin to established sufficient conditions for the existence of positive periodic solutions.4. from section 4, we had study Nonautonomous Stage-Structured two-species co-operative system with discrete delays and via employing continuation theorem of the coincidence degree theory developed by Gaines and Mawhin to established sufficient con-ditions for the existence of positive periodic solutions.5. from section 5, we had study nonautonomous n-species cooperative system with time varying delays and feedback controls and via employing continuation theorem of the coincidence degree theory developed by Gaines and Mawhin to established sufficient conditions for the existence of positive periodic solutions.6. from section 6, we had study nonautonomous n-species cooperative system with delays and impulses and via employing continuation theorem of the coincidence degree theory developed by Gaines and Mawhin to established sufficient conditions for the exis-tence of positive periodic solutions.7. in section 7, we did some discuss and conclusions about what we have studied in this paper.