Research On Internal Mechanism Of Enterprise Cluster Evolution

Enterprise cluster is an industrial organization,which is composed of many independent and correlative enterprises in a certain area.According to economic theory,enterprise cluster can be considered as a special economic system,thus,it also has many economic properties such as capital,investment,output and so on.The evolution of enterprise clusters is also affected by many economic factors such as investment time-delay,technology diffusion,competition and cooperation among enterprises in clusters.However,few studies investigate the evolution of enterprise clusters with time-delay,technology diffusion,competition and cooperation.Inspired by the observation,in this paper,we invesitgate the dynamic evolution of enterprise cluster with investment time-delay,technology diffusion and competition and cooperation.The main contents of this paper are as follow:(1)The evolution of enterprise clusters with investment time-delayis investigated.First,a novel evolution of enterprise clusters is proposed and the existence and boudedness of positive equilibrium are investigated.Then,the conditions of the Hopf bifurcation are established by regarding the time delay as the bifurcation parameter.In particular,by using the normal form theory and center manifold theorem of the partial differential equation,the normal forms are obtained,which determine the bifurcation direction and the stability of the periodic solutions.Finally,numerical results validate the obtained theorems.(2)By adding the diffusion effect in the proposed model,the evolution of enterprise clusters with investment time-delay and technology diffusion effect is investigated.First,the Turing instability conditions are obtained by analyisising the eigenvalue distribution of the corresponding characteristic equation.It is found that moderate technology diffusion in enterprise cluster is beneficial to the development of enterprise cluster.But excessive diffusion may lead to the disorder of enterprise cluster.Then,we find that the time delay can give rise to the Hopf bifurcation when the time delay passes a critical value under the moderate diffusion.The normal form of Hopf bifurcations is obtained by using the center manifold theorem and normal form theory of the partial differential equation,which can determine the bifurcation direction and the stability of the periodic solutions.Finally,numerical results not only validate the obtained theorems,but also show that the diffusion coefficients play a key role in the spatial pattern.With the diffusion coefficients increasing,different patterns appear.(3)The dynamic behaviors of enterprises cluster composed of two satellite enterprises and a dominant enterprise are investigated.First,the boudedness of positive equilibrium are investigated.Then,the conditions of the Hopf bifurcation are established by regarding the time delay as the bifurcation parameter.In particular,by using the normal form theory and center manifold theorem of the partial differential equation,the normal forms are obtained,which determine the bifurcation direction and the stability of the periodic solutions.It is found that when the production cycle exceeds the critical value,the system will change from stable to unstable,and then produce periodic solutions.(4)A case study of Chongqing automobile industry cluster is carried out.Firstly,the development status of Chongqing automobile industry cluster is summarized.Then,the paper builds the dynamic evolution models of Chongqing automobile industry cluster.The mechanism of action of capital,technology,enterprise competition and cooperation on the evolution of Chongqing automobile industry cluster is analyzed.Thirdly,by researching on the data of Chang'an automobile,which located in the center of Chongqing automobile industry cluster,the effect of time delay on the evolution of enterprise cluster is discussed.Finally,the paper analyses the constraints of the future development of Chongqing automobile industry cluster.