A comprehensive review of stability analysis of continuous-time recurrent neural networks

H Zhang, Z Wang, D Liu - IEEE Transactions on Neural …, 2014 - ieeexplore.ieee.org
Stability problems of continuous-time recurrent neural networks have been extensively
studied, and many papers have been published in the literature. The purpose of this paper is …

Bifurcation mechanism for fractional-order three-triangle multi-delayed neural networks

C Xu, Z Liu, P Li, J Yan, L Yao - Neural Processing Letters, 2023 - Springer
This article is basically concerned with the stability and Hopf bifurcation problem of fractional-
order three-triangle multi-delayed neural networks. Based on laplace transform, we obtain …

Fractional-order bidirectional associate memory (BAM) neural networks with multiple delays: The case of Hopf bifurcation

C Xu, Z Liu, M Liao, P Li, Q Xiao, S Yuan - Mathematics and Computers in …, 2021 - Elsevier
The stability and Hopf bifurcation have important effect on the design of neural networks. By
revealing the effect of parameters on the stability and Hopf bifurcation of neural networks, we …

Global asymptotic stability of a general class of recurrent neural networks with time-varying delays

J Cao, J Wang - IEEE Transactions on Circuits and Systems I …, 2003 - ieeexplore.ieee.org
In this paper, the existence and uniqueness of the equilibrium point and its global asymptotic
stability are discussed for a general class of recurrent neural networks with time-varying …

Stability in asymmetric Hopfield nets with transmission delays

K Gopalsamy, X He - Physica D: Nonlinear Phenomena, 1994 - Elsevier
Sufficient conditions are derived for the delay independent stability of the equilibria in
Hopfield's graded response networks of the type dx i (t)/dt=-bixi (t)+ Σ nj= 1 a ij fj (μ jxj (t-τ …

Impulsive control for existence, uniqueness, and global stability of periodic solutions of recurrent neural networks with discrete and continuously distributed delays

X Li, S Song - IEEE Transactions on neural networks and …, 2013 - ieeexplore.ieee.org
In this paper, a class of recurrent neural networks with discrete and continuously distributed
delays is considered. Sufficient conditions for the existence, uniqueness, and global …

Global asymptotic and robust stability of recurrent neural networks with time delays

J Cao, J Wang - IEEE Transactions on Circuits and Systems I …, 2005 - ieeexplore.ieee.org
In this paper, two related problems, global asymptotic stability (GAS) and global robust
stability (GRS) of neural networks with time delays, are studied. First, GAS of delayed neural …

Global exponential stability and periodicity of reaction–diffusion delayed recurrent neural networks with Dirichlet boundary conditions

JG Lu - Chaos, Solitons & Fractals, 2008 - Elsevier
In this paper, the global exponential stability and periodicity for a class of reaction–diffusion
delayed recurrent neural networks with Dirichlet boundary conditions are addressed by …

Stability and synchronization of discrete-time Markovian jumping neural networks with mixed mode-dependent time delays

Y Liu, Z Wang, J Liang, X Liu - IEEE Transactions on Neural …, 2009 - ieeexplore.ieee.org
In this paper, we introduce a new class of discrete-time neural networks (DNNs) with
Markovian jumping parameters as well as mode-dependent mixed time delays (both …

Delay-dependent exponential stability analysis of delayed neural networks: an LMI approach

X Liao, G Chen, EN Sanchez - Neural networks, 2002 - Elsevier
For neural networks with constant or time-varying delays, the problems of determining the
exponential stability and estimating the exponential convergence rate are studied in this …