Nonlinear Dynamics Alysis For The Improvement Of A Bio-economic Model

In this paper, we study the management of living marine resources by the method of complex nonlinear dynamics analysis. On the basis of learning the pioneering work, we improve the original model and give a detailed study of complex dynamic behavior. By introduce the average revenue function, some rationalization strategies on management issues are proposed.The paper is organized as follows. In chapter1we describe the theoretical and practical value of nonlinear dynamic system, the recent situation of marine living management, and the innovation of this paper. In chapter2we introduce some knowledge of nonlinear dynamics, including bifurcation, Lyapunov exponent, Lyapunov dimension and chaos. In chapter3we discuss the long-term dynamical behaviors of duopoly model. In chapter4we first prove the view that cooperative fishing mode can better protect the marine fishery resources. After that, we add an input factor to the original model, and discuss the existence and stability of equilibrium point, the phenomenon of period-doubling bifurcation and Hopf bifurcation in the new model. In addition, we use the largest Lyapunov exponent and Lyapunov dimension reveal that the improved model has a rich dynamical behavior, and use parameter adaptive feedback method to control chaos. At last we show some reasonable suggestions by the curve of revenue function. A short summary of the results is given in chapter5.