Intermittent Control for Finite-Time Bipartite Synchronization in Multilayer Signed Networks with Semi-Markovian Jumps

This paper investigates the finite-time bipartite synchronization (FTBS) problem in multilayer signed networks subject to semi-Markovian switching topologies and stochastic disturbances. A comprehensive framework is developed that simultaneously incorporates: (i) multilayer network with antagonistic interactions, (ii) semi-Markovian jump parameters, and (iii) stochastic noise effects, addressing key challenges in modeling heterogeneous, nonlinearly coupled systems operating in random environments. For the first time, FTBS is achieved through aperiodically intermittent control strategies. By combining graph-theoretic analysis with Lyapunov stability theory, some sufficient conditions for ensuring FTBS are established under the proposed control scheme. The theoretical results are rigorously verified through numerical simulations, demonstrating their feasibility and effectiveness.