Global Dissipativity for Quaternion Valued Inertial Neural Networks With Unbounded Time-Varying Delays

Abstract

In this article, the authors investigate the global and exponential dissipativity of quaternion-valued inertial neural networks (QVINNs) with mixed time-varying delays, without utilizing order reduction of inertial neural networks (INNs) and quaternion separation methods. Using innovative Lyapunov functional and inequality techniques, several fruitful sufficient criteria with multi-parameters are derived for QVINNs to ensure global dissipativity (GD), which generalizes and refines existing results. This article estimates the attractive sets and exponentially attractive sets globally. Unlike previous studies in which quaternion-valued neural networks (QVNNs) are separated into real-valued neural networks (RVNNs) and INNs are reduced into first-order systems, the foundation of this article rests upon approaches that diverge from the traditional methods of separation and order reduction. Unlike existing results on the GD of traditional neural networks (NNs) with bounded discrete time delays, this article focuses on INNs with unbounded discrete time-varying delays, which is more realistic because neurons consider their entire past rather than partial history within bounded time delays. In general, in exponential stability, synchronization, and dissipativity results, researchers typically impose an upper bound on the rate of convergence (Formula presented.), but in the present article, the authors investigate dissipativity criteria without such a restriction on the convergence rate in global exponential dissipativity (GED). Finally, to demonstrate the efficiency of our theoretical work, three consecutive examples are proposed to illustrate the effectiveness of the obtained results. The first two examples verify the proposed results, and the third one, related to QVNNs, redemonstrates the efficiency of storing true color image patterns. © 2025 John Wiley & Sons Ltd.