Periodic Solution Of Some Populations, Almost Periodic Solution And The Best Capture Problems

Biological resource is a kind of renewable resource, The optimal man-agement of renewable resources, which has a direct relationship to sustain-able development and exploitation has come into the ptoblems concerned by ecologists and economists and has been taken count of by academic field. The second part of this paper is mainly based on Gilpin-Ayala single-species growth model. We assume production function is Exβ(β is positive con-stant) then this model becomes,Optimal exploitation of the model is consideted. Optimal exploita-tion policies are determined. Relative results which have obtained in [1] are generalized. Results provide theory basis for objective management of renewable biological resources. Many objective problems often be trans-ferred to how to find the solution of Differential Equation (ODE, FDE). Especially on periodic solution and almost periodic solution of mathematics model. Extension of Yoshizawa Periodic Solution Theorem is mentioned in the third part. Nonautonomous three species predator-prey delay diffusion system with Michaelis-menten response function is studied.We obtain not only existence of periodic solution of the system, but also sufficient condition of positive periodic solution. In the fourth part, westructure Liapunov function to discuss the following three species predator-pery system.We obtain existence, uniqueness and global asymptotic stability of almost periodic solution.