Predefined finite time anti-phase synchronization studies of Hindmarsh–Rose neuron networks

Abstract

This article investigates the anti-phase synchronization of 5D Hindmarsh–Rose neuron networks (5D HRNNs) by using a predefined finite time approach. First, the global finite time stability of dynamic nonlinear systems is studied by using the inequality theorem. Then, by designing new negative predefined finite time controllers, in light of the Lyapunov functional method, novel predefined finite time anti-phase synchronization criteria are established for the considered 5D HRNNs. The anti-phase synchronization time of each state variable of two 5D HRNNs is different and can be defined in advance. Finally, two examples are used to verify the accuracy of the theorems.