Analysis of dynamical model for resource-based industry sustainable development

Abstract

This paper aims at the sustainable development of resource-based industry. First, one-dimensional discrete dynamic model is formulated by considering exploitation and protection of renewable resource simultaneously, and then it is extended to two-dimensional dynamic model by assuming that government carries on the dynamic management to the exploitation speed of resource. The conditions of the existence and local stability of positive equilibrium are derived. The threshold of output is given which ensures the resource is stabilized at a fixed value. The global analysis of both models is represented by determining the feasible domain of attractor. The stability of positive fixed point at flip bifurcation and Neimark-Sacker bifurcation is respectively investigated with center manifold theorem and normal form. We also verify the given conclusions by the method of numerical analysis. In the end, we argued that if the government implements the dynamic quota management for resource exploitation, 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 and wider output to meet the development of the industry.

Keywords:

• Resource-based industry
• sustainable development
• flip bifurcation
• Neimark bifurcation
• center-manifold
• normal form
• feasible domain

AMS Subject Classifications:

• 37N99
• 58K30
• 91A26
• 91A80 MASS:110.51
• 790.4950

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by Central Special Fund [YCZW15122]; National Natural Science Foundation of China [grant number 10871209].