Global Exponential Stability for Complex-Valued Recurrent Neural Networks With Asynchronous Time Delays

TL;DR

This paper establishes less restrictive conditions for the global exponential stability of complex-valued recurrent neural networks with asynchronous delays, using a novel approach that decomposes the networks into real and imaginary parts and employs generalized norms.

Contribution

It introduces a new stability analysis method for complex-valued neural networks with asynchronous delays, directly proving exponential convergence without prior existence and uniqueness results.

Findings

Derived sufficient conditions for stability using generalized norms

Extended previous results to more general asynchronous delay models

Numerical simulations confirm theoretical stability conditions

Abstract

In this paper, we investigate the global exponential stability for complex-valued recurrent neural networks with asynchronous time delays by decomposing complex-valued networks to real and imaginary parts and construct an equivalent real-valued system. The network model is described by a continuous-time equation. There are two main differences of this paper with previous works: (1), time delays can be asynchronous, i.e., delays between different nodes are different, which makes our model more general; (2), we prove the exponential convergence directly, while the existence and uniqueness of the equilibrium point is just a direct consequence of the exponential convergence. By using three generalized norms, we present some sufficient conditions for the uniqueness and global exponential stability of the equilibrium point for delayed complex-valued neural networks. These conditions in our results are less restrictive because of our consideration of the excitatory and inhibitory effects between neurons, so previous works of other researchers can be extended. Finally, some numerical simulations are given to demonstrate the correctness of our obtained results.