Studies On A Class Of Semi-continuous Dynamical System About The Resource-based Industry Cluster

Based on the fact that the industrial cluster development and the population evolution process have a certain similarity, the relationship between the upstream and downstream enterprises in the resource-based industry cluster is described by using population ecology predator-prey model. A class of impulsive state dynamical systems is formulated by using the ideas of impulsive state feedback control.The existence of order-1homoclinic cycle is firstly discussed. By the bifurcation of homoclinic cycle, the existence of order-1periodic solution is discussed to show the periodicity of the enterprise development under impulsive state control. At the same time, it is pointed out that the system has two kinds of order-1periodic solutions. The uniqueness of periodic solutions of the order-1periodic solution of type I is proved by using compression mapping, and the sufficient conditions for the orbital stability of order-1periodic solution is given by the analogue of Poincare criterion. Finally, the corresponding numerical simulation and discussion are given.