Dynamic Analysis of a Competition‐Cooperation Enterprise Cluster with Core‐Satellite Structure and Time Delay

Core and satellite structure is one of the common structures in enterprise clusters. In core and satellite structure, there are one core enterprise and at least two satellite enterprises. There exist a competitive relationship between satellite enterprises and a cooperative relationship between satellite enterprise and core enterprise. However, the dynamic evolution of competition‐cooperation enterprise clusters with core‐satellite structure is not well understood. In this paper, a novel competition‐cooperation enterprise cluster model with core‐satellite structure is proposed. The boundedness of the positive equilibrium is investigated. It is found that there exists upper bound of both core enterprise output and satellite enterprise output and the upper bound of core enterprise not only depends on its own production capacity but also depends on the production capacity of two satellite enterprises. Then, by selecting the production period as bifurcating parameter, the conditions of local stability and Hopf bifurcation are obtained. Once the production period passes a critical value, the output of both core enterprise and satellite enterprise loses stability and displays periodic fluctuations. This may lead to the decline of efficiency of enterprise and resource mismatch. Furthermore, the fluctuation properties are studied. Finally, a numerical example is presented to show the effectiveness of theorem.