Taming chimeras in multiplex networks of coupled oscillators based on multi-agent deep reinforcement learning

We propose a method based on the multi-agent soft actor–critic (MASAC) algorithm for taming chimera states in two-layer multiplex networks. In the method, two agents are designed, where one is responsible for observing and controlling the accessible layer and the other dedicated to monitoring the target layer and adaptively adjusting the interlayer coupling strengths accordingly. Through cooperation, the two agents can achieve indirect control of the desired chimera state in the inaccessible target layer, despite being unavailable for direct access. The method employs the centralized training and decentralized execution framework, to overcome the difficulty of implementing control without simultaneous observation of all layers. Furthermore, pinning control is introduced when controlling the accessible layer. In this MASAC-based method combined with pinning control, the control mechanism of chimera states does not arise from synchronization, but relates to cooperation between two designed agents. Therefore, the method works even without the desired chimera state in the accessible layer. Results demonstrate the effectiveness and robustness of the MASAC-based method, both with and without pinning control, across varying system sizes and ratios of controlled nodes. The MASAC-based method combined with pinning control remains effective even when only 10% of the nodes in the accessible layer are actively controlled.