Synchronization regulation in multiplex neuron networks via dynamic learning of synchronization

Synchronization phenomena are pervasive in both natural and engineered systems and have recently attracted increasing attention in the context of multiplex networks. To achieve efficient regulation of synchronization behaviour in multiplex networks, this study proposes an adaptive control framework that integrates dynamic learning synchronization (DLS) with the alternating direction method of multipliers (ADMM), termed DLS-ADMM. The method adaptively adjusts node connection weights by tracking their dynamic states, while the ADMM optimization effectively constrains the amplitude of weight updates. We systematically analyse the regulation capabilities of DLS-ADMM in multiplex small-world networks, focusing on global synchronization, local synchronization induction, learning node distribution, and cross-layer coordinated control. Results demonstrate that DLS-ADMM not only rapidly enhances network synchronization and enables recovery after perturbations but also flexibly induces synchronization in other layers, with the effectiveness significantly influenced by inter-layer coupling strength and learning region extent. Furthermore, the realization of bidirectional synchronization further confirms the flexibility and broad applicability of the method. DLS-ADMM provides an efficient and controllable solution for synchronization regulation in multiplex networks, offering new theoretical and methodological support for brain-inspired modelling and intelligent neural control strategy design.