Absolute exponential stability of recurrent neural networks with Lipschitz-continuous activation functions and time delays

Authors:
Jinde Cao;Jun Wang
Affiliations:
Department of Mathematics, Southeast University, Nanjing 210096 Jiangsu, China;Department of Automation and Computer-Aided Engineering, The Chinese University of Hong Kong Shatin, New Territories, Hong Kong, China
Venue:
Neural Networks
Year:
2004

Citing 7
Cited 40

The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods

The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods
Exponential stability and a systematic synthesis of a neural network for quadratic minimization

Neural Networks
Frustration, stability, and delay-induced oscillations in a neural network model

SIAM Journal on Applied Mathematics
Bifurcations, stability, and monotonicity properties of a delayed neural network model

Physica D
Effect of delay on the boundary of the basin of attraction in a system of two neurons

Neural Networks
Stability analysis of delayed cellular neural networks

Neural Networks
Global stability for cellular neural networks with time delay

IEEE Transactions on Neural Networks

Analysis of global exponential stability and periodic solutions of neural networks with time-varying delays

Neural Networks
Global exponential stability of generalized recurrent neural networks with discrete and distributed delays

Neural Networks
Hopf bifurcation and stability for a delayed tri-neuron network model

Journal of Computational and Applied Mathematics
Global exponential stability of impulsive high-order BAM neural networks with time-varying delays

Neural Networks
Boundedness and Stability for Integrodifferential Equations Modeling Neural Field with Time Delay

Neural Computation
Global robust stability of neural networks with time varying delays

Journal of Computational and Applied Mathematics
New criteria of global exponential stability for a class of generalized neural networks with time-varying delays

Neurocomputing
An LMI approach to global asymptotic stability of the delayed Cohen-Grossberg neural network via nonsmooth analysis

Neural Networks
Stability of Cohen-Grossberg neural networks with time-varying delays

Neural Networks
Letters: Exponential state estimation for recurrent neural networks with distributed delays

Neurocomputing
Asymptotic behavior of discrete solutions to delayed neural networks with impulses

Neurocomputing
pth moment stability analysis of stochastic recurrent neural networks with time-varying delays

Information Sciences: an International Journal
Exponential stability preservation in discrete-time analogues of artificial neural networks with distributed delays

Journal of Computational and Applied Mathematics
Dynamic Analysis of Stochastic Recurrent Neural Networks

Neural Processing Letters
On the distribution of the roots of a fifth degree exponential polynomial with application to a delayed neural network model

Neurocomputing
Robust stability criteria for interval Cohen-Grossberg neural networks with time varying delay

Neurocomputing
Robust stability analysis of generalized neural networks with multiple discrete delays and multiple distributed delays

Neurocomputing
Delay-dependent stability of neutral type neural networks with distributed delays

Neurocomputing
Global asymptotic stability of delayed neural networks with discontinuous neuron activations

Neurocomputing
Delay-dependent robust stability for uncertain stochastic fuzzy Hopfield neural networks with time-varying delays

Fuzzy Sets and Systems
Exponential periodicity and stability of neural networks with reaction-diffusion terms and both variable and unbounded delays

Computers & Mathematics with Applications
Dynamic associative memory, based on open recurrent neural network

IJCNN'09 Proceedings of the 2009 international joint conference on Neural Networks
The Hopf bifurcation analysis on a time-delayed recurrent neural network in the frequency domain

Neurocomputing
Dynamics of high-order Hopfield neural networks with time delays

Neurocomputing
Global exponential stability of discrete-time Cohen-Grossberg neural networks

Neurocomputing
Absolutely exponential stability of Cohen-Grossberg neural networks with unbounded delays

Neurocomputing
Delayed Lagrangian neural networks for solving convex programming problems

Neurocomputing
Exponential stability of delayed Cellular Neural Networks with large impulses

International Journal of Systems, Control and Communications
The Bogdanov-Takens bifurcation analysis on a three dimensional recurrent neural network

Neurocomputing
New Results on Robust Exponential Stability of Uncertain Stochastic Neural Networks with Mixed Time-Varying Delays

Neural Processing Letters
Global exponential stability of recurrent neural networks with infinite time-varying delays and reaction-diffusion terms

ISNN'05 Proceedings of the Second international conference on Advances in Neural Networks - Volume Part I
Exponential stability of fuzzy cellular neural networks with unbounded delay

ISNN'05 Proceedings of the Second international conference on Advances in Neural Networks - Volume Part I
Global exponential stability of hopfield neural networks with impulsive effects

ISNN'05 Proceedings of the Second international conference on Advances in Neural Networks - Volume Part I
Universal approach to study delayed dynamical systems

ICNC'05 Proceedings of the First international conference on Advances in Natural Computation - Volume Part I
Global exponential stability of a class of generalized neural networks with variable coefficients and distributed delays

ICIC'05 Proceedings of the 2005 international conference on Advances in Intelligent Computing - Volume Part I
Existence and global convergence of periodic solution of delayed neural networks

Mathematical and Computer Modelling: An International Journal
Global attracting set for non-autonomous neutral type neural networks with distributed delays

Neurocomputing
Global exponential periodicity and stability of a class of memristor-based recurrent neural networks with multiple delays

Information Sciences: an International Journal
Mean square exponential stability for discrete-time stochastic switched static neural networks with randomly occurring nonlinearities and stochastic delay

Neurocomputing
pth Moment Exponential Stability of Stochastic Recurrent Neural Networks with Markovian Switching

Neural Processing Letters

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper investigates the absolute exponential stability of a general class of delayed neural networks, which require the activation functions to be partially Lipschitz continuous and monotone nondecreasing only, but not necessarily differentiable or bounded. Three new sufficient conditions are derived to ascertain whether or not the equilibrium points of the delayed neural networks with additively diagonally stable interconnection matrices are absolutely exponentially stable by using delay Halanay-type inequality and Lyapuno v function. The stability criteria are also suitable for delayed optimization neural networks and delayed cellular neural networks whose activation functions are often nondifferentiable or unbounded. The results herein answer a question: if a neural network without any delay is absolutely exponentially stable, then under what additional conditions, the neural networks with delay is also absolutely exponentially stable.