Fixed-time synchronization of quaternion-valued neural networks with impulsive effects: A non-decomposition method

This paper studies the fixed-time synchronization of a class of quaternion-valued neural networks (QVNNs) with time delays and impulses. In contrast to some existing decomposition methods for studying this problem, this paper presents several strategies to simplify the implicit Lyapunov function method from both controller and implicit function equation perspectives. The benefits of these strategies are, in the first strategy, the controller does not contain the Lyapunov function so that the controller will be more general, and in the second strategy, the implicit function equation is simpler so that the restriction on the bounded Lyapunov function can be dispensed with, which also makes the technique of handling time delays simpler. Furthermore, three sufficient conditions for fixed-time synchronization of the above QVNN are presented, despite the impulsive influence. Finally, we verify the feasibility of our methods with three examples.