Global $\mu$-stability and finite-time control of octonion-valued neural networks with unbounded delays

TL;DR

This paper investigates the stability and finite-time control of octonion-valued neural networks with unbounded delays, providing new criteria for stability and demonstrating their effectiveness through simulations.

Contribution

It introduces a novel approach by decomposing OVNNs into real-valued networks and establishes new stability criteria, including adaptive finite-time stability, for networks with unbounded delays.

Findings

Established sufficient criteria for existence and stability of OVNNs.

Proposed controllers to achieve finite-time stability.

Validated theoretical results with simulation examples.

Abstract

Octonion-valued neural networks (OVNNs) are a type of neural networks for which the states and weights are octonions. In this paper, the global $\mu$-stability and finite-time stability problems for octonion-valued neural networks are considered under unbounded and asynchronous time-varying delays. To avoid the non-communicative and non-associative multiplication feature of the octonions, we firstly decompose the OVNNs into eight real-valued neural networks (RVNNs) equivalently. Through the use of generalized norm and the Cauchy convergence principle, we obtain the sufficient criteria which assure the existence, uniqueness of the equilibrium point and global $\mu$-stability of OVNNs. By adding controllers, the criteria to ensure the finite-time stability for OVNNs are presented by dividing the analysis of finite-time stability process into two phases. Furthermore, we also prove the adaptive finite time stability theory of above networks. At last, the simulation results of specified examples is given to substantiate the effectiveness and correctness of the theoretical results.