Exponential and finite/fixed-time synchronization of quaternion-valued Cohen-Grossberg inertial neural networks with proportional-delayed by non-separated method with imperfect order theory

Abstract

Abstract In this paper, exponential and finite/fixed-time synchronization of quaternion-valued Cohen-Grossberg inertial neural network with proportional-delayed is investigated. In order to study the convergence of quaternion-value system, we proposed the imperfect order theory. Accordingly quaternion-value Lyapunov function are proposed and utilized to study the synchronization of the neural network. Several lemmas are introduced and proved for the later synchronization study. Unlike the most commonly used separated method for quaternion-value network, with the help of our imperfect order theory, we adopt a non-separated method to construct the controller and analyze the quaternion value Lyapunov function directly. Numerical simulations are presented to indicate the effectiveness of the proposed method.