Fixed-time synchronization of octonion-valued neural networks with mixed delays

Abstract

This work emphasizes the fixed-time synchronization (FTS) of a specific class of octonion-valued neural networks (OVNNs), which incorporate discrete and distributed time delays. This study also establishes several norm properties for the octonion domains and explores FTS and fixed-time projective synchronization (FTPS) in OVNNs having mixed time delays by a suitable choice of the Lyapunov function, controllers and the one norm property. Unlike previous research on the decomposition of neural networks with octonion-valued and quaternion-valued components, this study introduces an enhanced one-norm method based on the non-separation approach. It employs a direct analytical approach to address two synchronization challenges using several norm properties. The computational complexity is reduced to provide less conservative results for OVNNs. This article analyzes various properties of the one norm of octonion domains and introduces effective controllers for achieving FTS and FTPS between the drive and response systems of OVNNs. The present article also establishes results in a compact and more generalized form using one norm criteria, which are easily verifiable to ensure synchronization, even with mixed time delays, which can be achieved within fixed time intervals. The settling time in each case illustrates its effectiveness compared to the existing results in a more straightforward way through a unique analytical process and more versatile activation functions. Finally, the theoretical results are validated through two numerical examples, with the overall results presented and discussed. Additionally, OVNNs are employed to demonstrate their effectiveness in storing and retrieving true-color images. This application showcases the ability of OVNNs to handle high-dimensional data representations, particularly in contexts where color channels and spatial features are strongly interrelated. The results highlight the robustness and efficiency of the proposed OVNNs framework, confirming its potential for advanced multidimensional data processing tasks.