Cluster synchronization of fractional-order two-layer networks and application in image encryption/decryption

In this paper, a type of fractional-order two-layer network model is constructed, wherein each layer in the network exhibits distinct topology. Subsequently, the cluster synchronization problem of fractional-order two-layer networks is investigated through a two-step approach. The initial step involves the implementation of finite-time cluster synchronization in the first layer by utilizing a fractional-order finite-time convergence lemma. Based upon this, the second step employs a novel approach of collectively treating the nodes within the same cluster in the first layer, thereby offering a significant insight for analyzing fractional-order two-layer networks cluster synchronization. In addition, the paper proposes a novel encryption/decryption scheme based on the cluster synchronization of fractional-order two-layer networks. By leveraging the complexity of chaotic sequences generated by fractional-order two-layer networks, the security of the encryption/decryption strategy is enhanced. Furthermore, three illustrative examples are provided to validate the theoretical findings.