Finite-time bipartite synchronization of multi-layer networks via intermittent adaptive control

This paper investigates bipartite synchronization in multi-layer networks by proposing an aperiodic intermittent adaptive pinning control strategy. The proposed approach integrates intermittent adaptive mechanisms with pinning control techniques, minimizing direct intervention to a subset of most nodes. Extending the analysis to finite-time synchronization scenarios, this study further proposes a novel control strategy to achieve synchronization within finite time through global intermittent control protocols. Theoretical analysis of synchronization errors establishes sufficient conditions for both bipartite synchronization and finite-time bipartite synchronization based on Lyapunov stability theory. Numerical simulations validate the control protocol’s effectiveness in reducing synchronization time. The aperiodic design of the control protocol further enhances its practicality by eliminating periodicity requirements, making it adaptable to real-world network dynamics.