Lagrange synchronization of nonidentical discrete-time fractional-order quaternion-valued neural networks with time delays

This paper is devoted to the study of Lagrange synchronization of nonidentical discrete-time fractional-order quaternion-valued neural networks (DFQNNs) with time delays. First, a new inequality is established by using the definition and operational principles of quaternion sign function. Next, in order to achieve Lagrange synchronization, a state feedback controller is designed. And then, some criteria are derived to guarantee Lagrange synchronization of nonidentical DFQNNs by employing Lyapunov method and fractional difference theory as well as quaternion properties. Finally, the validity and feasibility of the theoretical results are verified by numerical simulations.