The feedback strength changing rate of pinning control systems and its application to key node identification

Identifying key nodes in pinning control systems is crucial for ensuring system reliability and safety. Existing algorithms typically use Lyapunov exponents to assess stability conditions, while neglecting the impact of feedback and coupling strengths of the pinning control system. This results in poor identification of node importance in pinning control systems. In this paper, based on local stability theory of Lyapunov exponents, the change rate of feedback strength range relative to coupling strength is firstly introduced and a novel key node identification algorithm is developed accordingly. This algorithm aims to enhance the identification of node importance and its impact on system control performance. Under the premise of maintaining system stability, the algorithm also allows for a reasonable selection of the feedback strength range for the nodes. Experimental results demonstrate that the proposed algorithm effectively captures changes in coupling strength, assesses the impact on feedback strength range, and demonstrates efficacy in node importance identification across multiple datasets. The datasets used in the experiments broadly cover common system types which can be used for a comprehensive evaluation of the proposed method, including biological, technological, physical, and artificial systems.