The Analysis of Social Power Evolution in Cooperation Networks Based on the Interval Reflected Appraisals

This paper proposes a mathematical model based on interval reflective evaluation to investigate the evolution of social power within cooperative networks. On a single time scale, opinion dynamics adhere to the Friedkin-Johnsen (F-J) model, incorporating iterative self-weighting updates. By employing matrix vectorization, the system is reformulated into a nonlinear mapping. Then, the Banach Fixed Point Theorem substantiates the existence of an equilibrium point, while its uniqueness and convergence depend on individual susceptibility. Some numerical simulations validate the theoretical findings.