Synchronization of Fractional-Order Quaternion-Valued Coupled Neural Networks via Hybrid Control Approach

Without separating the fractional-order quaternion-valued coupled neural networks (FQVCNNs) into four real-valued systems, synchronization for FQVCNNs is investigated in this paper. Firstly, a hybrid control approach including internal drive and external control is considered. To be specific, based on local information of the nodes’ dynamics, edge-based fractional-order adaptive technique for coupling weights and adaptive feedback controllers are simultaneously applied to synchronize the FQVCNNs to the desired trajectory. Particularly, some new analytical approaches for fractional-order adaptive schemes, including the method of contradiction, the Mean Value Theorem are developed to establish synchronization criteria of the network system. Finally, a numerical simulation is provided to illustrate the validity of theoretical results.