Fixed-time synchronization of quaternion-valued neural networks

In this paper, the fixed-time synchronization problem of quaternion-valued neural networks is investigated. Different from the finite-time synchronization related to the initial conditions, the settling time of fixed-time synchronization can be changed properly according to the actual needs. The fixed-time synchronization of quaternion-valued neural networks is firstly studied by adding the new nonlinear feedback controllers and employing the theorem of fixed-time stability. The quaternion-valued neural network is addressed by dividing the system under investigation into four real-valued parts. Then based on related theorem of fixed-time stability, and selecting the appropriate controllers and Lyapunov function, sufficient conditions of fixed-time synchronization for quaternion-valued neural networks are obtained. In the same way, the results of finite-time synchronization can also be got. Finally, one numerical example is provided to illustrate the effectiveness of the proposed results. (C) 2019 Elsevier B.V. All rights reserved.