Abstract：Aiming at the analysis of the evolution trend of enterprise innovation time-delay evolutionary game under switching topology, firstly, the cooperative game network is constructed by treating the enterprise as a node and using edges to represent the correlation between enterprises. Then, the model of the evolutionary game with time delays of enterprise cooperative innovation under switching topology is established. Secondly, the revenue of the game, the evolution of the strategic profile and the switching of game networks are formulated separately by semi-tensor product. The algebraic expression of the process of evolutionary game enterprise innovation under switching topology is obtained, and the characteristics of game evolution are analyzed. Thirdly, the control input is designed, the necessary and sufficient conditions for all enterprises to participate in cooperative innovation are obtained. Finally, example is provided to illustrate the theoretical result.
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