Research on pinning control of complex networks based on node group selection

Complex network pinning synchronization control aims to achieve synchronization of all nodes by exerting control over a few critical nodes in the network. This paper proposes an optimal control node group selection algorithm based on the theory of pinning control, using the minimum nonzero eigenvalue of the grounded Laplacian matrix of the node group as the evaluation metric to find the optimal controlled node group. According to the criteria of network synchronization, given the dynamics of individual nodes and the coupling strength between them, the larger the minimum nonzero eigenvalue of the grounded Laplacian matrix of the node group, the more important the node group is in network synchronization. Building upon this foundation, combining the simulated annealing algorithm with the optimal control node group selection algorithm enables the search for approximate optimal solutions in larger-scale networks. Therefore, compared to commonly used control node group selection algorithms, this algorithm in this paper can more accurately identify an optimal controlled node group. Finally, simulation validation is conducted, confirming the accuracy and effectiveness of the results through practical network verification.