Fixed-time synchronization for quaternion-valued memristor-based neural networks with mixed delays

TL;DR

This paper develops a direct analytical approach using one-norm and Lyapunov functions to achieve fixed-time synchronization in quaternion-valued memristor neural networks with mixed delays, providing explicit settling time estimates.

Contribution

It introduces a novel direct method for fixed-time synchronization of quaternion-valued memristor neural networks without decomposition, handling discontinuities with set-valued maps and differential inclusions.

Findings

Established criteria for fixed-time synchronization

Derived explicit settling time estimates

Validated results with numerical simulations

Abstract

In this paper, the fixed-time synchronization (FXTSYN) of unilateral coefficients quaternion-valued memristor-based neural networks (UCQVMNNs) with mixed delays is investigated. Instead of decomposition, a direct analytical method is proposed to achieve FXTSYN of UCQVMNNs using one-norm smoothly. Then apply the set-valued map and the differential inclusion theorem to handle discontinuity problems of drive-response systems. The novel nonlinear controllers together with the Lyapunov function are designed to achieve the control goal. Using the FXTSYN theory and inequality techniques, some criteria of FXTSYN for UCQVMNNs are given. Furthermore, the estimated settling time is obtained explicitly. Finally, numerical simulations are presented to demonstrate the correctness, effectiveness and practicability of the obtained theoretical results.