The Analysis Of Discrete Dynamical Model For Sustainable Development Of Resource-based Industry

On the basis of the dynamic equation of optimal model for the sustainable development of resources – economy which presented by Ming-yi Chen et al., first of all, we assume that the resource development speed remain unchanged, and construct a one-dimensional discrete dynamic system which describe the interaction between resource stock and production, then discuss the effect of output to the sustainable utilization of resources. Secondly, if government implements dynamic management of resource development speed, we construct a two-dimensional discrete dynamic system which describe the resource stock and the development pace of resource, and study the effect of output to the sustainable utilization of resources under the control of resources development speed.First, we simply introduce the background and significance of sustainable development of resource-based industry, and the research content, research method and content arrangement of this paper are given so that we can understand the paper on a whole.Secondly, in view of the one-dimensional model, we use mathematical analysis to analyze the existence of fixed point and local stability, and give relevant theorems. The theorem is proved by numerical simulation. We use the irreversible mapping theory of single value point to study the the global bifurcation of feasible domain, which caused by the change of output, and map out the feasible domain. In view of the two-dimensional model, we use mathematical analysis to analyze the existence of fixed point and local stability, in particular, we use center-manifold theorem and canonical form to investigate the stability of the positive fixed point, and give relevant theorems. The theorem is proved by numerical simulation. We draw the Lyapunov exponent and Time series plot of the one-dimensional system and the two-dimensional system to prove that the two-dimensional system can control the chaotic behavior of the one-dimensional system; then we use the Critical Line theory of two-dimensional continuous noninvertible mapping system to globally analysis the discrete two-dimensional system, and map out the feasible domain. Finally, we use the theory of topological horseshoe to study chaotic behavior, and according to the existence conditions of topological horseshoe and corresponding search method put forward by professor Li and professor Yang, we finally find a topological horseshoe in the chaotic attractor with the aid of Matlab toolbox HsTool when take certain parameters, and prove that the two-dimensional system is chaotic.In the end, we argued that if the government controls the speed of exploiting resources, not only can we maintain a certain stock of resources so that people can get more resources permanently but also we can ensure a higher yield.