Impulsive Fixed-Time Bipartite Synchronization of Fuzzy Multilayer Signed Networks

This article addresses the problem of fixed-time bipartite synchronization (FxTBS) of signed networks (SNs) affected by impulses. First, this article constructs a model of SNs that captures the multilayer properties of the network and takes into account the influence of nonlinear coupling strengths between nodes. To overcome the challenges brought by the introduction of nonlinear coupling strengths, this article adopts a Takagi–Sugeno fuzzy model to characterize the nonlinear variation of coupling strengths reasonably. Then, in the framework of average impulsive interval applicable to a wider range of impulsive signals, this article proposes a novel method for analyzing the fixed-time stability of impulsive systems, which not only loosens the restriction of the derivative of the Lyapunov function in the existing studies, but also gives a more accurate estimation of the settling time, and more importantly, provides a theoretical basis for designing appropriate impulsive signals to modulate the dynamic behavior of SNs toward achieving the desired goal. Based on the newly suggested method, this article derives a unified synchronization criterion suitable for evaluating the implementation of FxTBS of SNs under both desynchronizing and synchronizing impulses. Finally, this article visualizes the correctness of the aforementioned theoretical results utilizing a widely used numerical example.