Nonlinear Dynamics Analysis For The Establishment Of A Marine Fishery Resources Model

It is rich in Marine fishery resources in China. But Marine fishery resources are over-exploited and fishing production and economic benefits decrease dramati-cally with the development of coastal economy and the growth of population. This article focuses on their modeling and their long-time adjustment process with cap-turing, stocking and delay coupling. It is known that delay effect can not be neglected. Based on the classic Logistic model and Gains profit functions, a three-dimensional model of the fishery resources is proposed and rich dynamics is to de determined:the stability of fixed points by the Schur-Cohn-Jury criterion, bifur-cation analysis by calculating the center manifolds and the normal forms,including period-doubling bifurcations, trans-critical bifurcations and Neimark-Sacker bifur-cations etc. Chaotic behavior is determined by calculating the largest Lyapunov exponent.By the calculation of the average profit, we find that it almost remains con-stant until there occur bifurcations, and decreases dramatically when there exist chaotic behavior. This motivates us to adopt adaptive chaos controllers to bring the chaotic system into a regular one. Finally we use Gordon theory to find out that what is the optimal capturing and stocking strategy of keeping the fishing resources stable and gaining the economic equilibrium. In order to study the role of the motility of the fishery resources on the total marine fishery products, we propose a six dimensional model and its long-time behavior is also discussed. In addition, a3n-dimensional model with random topological architectures is pro-posed which will be a future topic.