GLOBAL EXPONENTIAL STABILITY AND PERIODIC OSCILLATIONS OF REACTION–DIFFUSION BAM NEURAL NETWORKS WITH PERIODIC COEFFICIENTS AND GENERAL DELAYS

2007 ◽  
Vol 17 (01) ◽  
pp. 129-142 ◽  
Author(s):  
QINGHUA ZHOU ◽  
JIANHUA SUN ◽  
GUANRONG CHEN
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Activation Functions ◽  
Bidirectional Associative Memory ◽  
Connection Weight ◽  
Periodic Coefficients ◽  
Delay Dependent

For a large class of reaction–diffusion bidirectional associative memory (RDBAM) neural networks with periodic coefficients and general delays, several new delay-dependent or delay-independent sufficient conditions ensuring the existence and global exponential stability of a unique periodic solution are given, by constructing suitable Lyapunov functionals and employing some analytic techniques such as Poincaré mapping. The presented conditions are easily verifiable and useful in the design and applications of RDBAM neural networks. Moreover, the employed analytic techniques do not require the symmetry of the bidirectional connection weight matrix, the boundedness, monotonicity and differentiability of activation functions of the network. In several ways, the results generalize and improve those established in the current literature.

scholarly journals Preserving Global Exponential Stability of Hybrid BAM Neural Networks with Reaction Diffusion Terms in the Presence of Stochastic Noise and Connection Weight Matrices Uncertainty

2014 ◽  
Vol 2014 ◽  
pp. 1-17
Author(s):  
Yan Li ◽  
Yi Shen
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Global Exponential Stability ◽  
Reaction Diffusion ◽  
Stochastic Noise ◽  
Bam Neural Networks ◽  
Connection Weight ◽  
Exponentially Stable ◽  
The Neural Networks ◽  
The Impact

We study the impact of stochastic noise and connection weight matrices uncertainty on global exponential stability of hybrid BAM neural networks with reaction diffusion terms. Given globally exponentially stable hybrid BAM neural networks with reaction diffusion terms, the question to be addressed here is how much stochastic noise and connection weights matrices uncertainty the neural networks can tolerate while maintaining global exponential stability. The upper threshold of stochastic noise and connection weights matrices uncertainty is defined by using the transcendental equations. We find that the perturbed hybrid BAM neural networks with reaction diffusion terms preserve global exponential stability if the intensity of both stochastic noise and connection weights matrices uncertainty is smaller than the defined upper threshold. A numerical example is also provided to illustrate the theoretical conclusion.

Global exponential stability of cellular neural networks with multi-proportional delays

2015 ◽  
Vol 08 (06) ◽  
pp. 1550071 ◽  
Author(s):  
Liqun Zhou ◽  
Yanyan Zhang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Cellular Neural Networks ◽  
Varying Coefficients ◽  
Proportional Delays ◽  
Time Varying Coefficients ◽  
Delay Differential ◽  
Delay Dependent

In this paper, a class of cellular neural networks (CNNs) with multi-proportional delays is studied. The nonlinear transformation yi(t) = xi( e t) transforms a class of CNNs with multi-proportional delays into a class of CNNs with multi-constant delays and time-varying coefficients. By applying Brouwer fixed point theorem and constructing the delay differential inequality, several delay-independent and delay-dependent sufficient conditions are derived for ensuring the existence, uniqueness and global exponential stability of equilibrium of the system and the exponentially convergent rate is estimated. And several examples and their simulations are given to illustrate the effectiveness of obtained results.

EXPONENTIAL STABILITY OF REACTION–DIFFUSION FUZZY RECURRENT NEURAL NETWORKS WITH TIME-VARYING DELAYS

2007 ◽  
Vol 17 (09) ◽  
pp. 3099-3108 ◽  
Author(s):  
QINGHUA ZHOU ◽  
LI WAN ◽  
JIANHUA SUN
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Recurrent Neural Networks ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Time Varying ◽  
Matrix Properties ◽  
Inequality Technique ◽  
Delay Dependent ◽  
Theoretical Results

Exponential stability of reaction–diffusion fuzzy recurrent neural networks (RDFRNNs) with time-varying delays are considered. By using the method of variational parameters, M-matrix properties and inequality technique, some delay-independent or delay-dependent sufficient conditions for guaranteeing the exponential stability of an equilibrium solution are obtained. One example is given to demonstrate the theoretical results.

scholarly journals Global Exponential Stability Criteria for Bidirectional Associative Memory Neural Networks with Time-Varying Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
J. Thipcha ◽  
P. Niamsup
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Associative Memory ◽  
Global Exponential Stability ◽  
Linear Matrix ◽  
Time Varying ◽  
Stability Criteria ◽  
Bidirectional Associative Memory ◽  
Lower And Upper Bounds ◽  
Delay Dependent

The global exponential stability for bidirectional associative memory neural networks with time-varying delays is studied. In our study, the lower and upper bounds of the activation functions are allowed to be either positive, negative, or zero. By constructing new and improved Lyapunov-Krasovskii functional and introducing free-weighting matrices, a new and improved delay-dependent exponential stability for BAM neural networks with time-varying delays is derived in the form of linear matrix inequality (LMI). Numerical examples are given to demonstrate that the derived condition is less conservative than some existing results given in the literature.

scholarly journals Global Exponential Stability and Periodicity of Nonautonomous Impulsive Neural Networks with Time-Varying Delays and Reaction-Diffusion Terms

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Weiyi Hu ◽  
Kelin Li
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Global Exponential Stability ◽  
Fixed Point Theory ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Point Theory ◽  
Time Varying ◽  
Nonautonomous Systems ◽  
Inequality Techniques

In this paper, we investigate the global exponential stability and periodicity of nonautonomous cellular neural networks with reaction-diffusion, impulses, and time-varying delays. By establishing a new differential inequality for nonautonomous systems, using the properties of M-matrix and inequality techniques, some new sufficient conditions for the global exponential stability of the system are obtained. Moreover, sufficient conditions for the periodic solutions of the system are obtained by using the Poincare mapping and the fixed point theory. The validity and superiority of the main results are verified by numerical examples and simulations.

GLOBAL EXPONENTIAL STABILITY OF HIGH-ORDER BAM NEURAL NETWORKS WITH REACTION–DIFFUSION TERMS

2010 ◽  
Vol 20 (10) ◽  
pp. 3209-3223 ◽  
Author(s):  
FENG-YAN ZHOU ◽  
CHENG-RONG MA
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Time Delays ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Mean Value ◽  
High Order ◽  
Mean Value Theorem ◽  
Bam Neural Networks

The global exponential stability is studied for a class of high-order bi-directional associative memory (BAM) neural networks with time delays and reaction–diffusion terms. By constructing suitable Lyapunov functional, using differential mean value theorem and homeomorphism, several sufficient conditions guaranteeing the existence, uniqueness and global exponential stability of high-order BAM neural networks with time delays and reaction–diffusion terms are given. Two illustrative examples are also given in the end to show the effectiveness of our results.

scholarly journals Impulsive Disturbances on the Dynamical Behavior of Complex-Valued Cohen-Grossberg Neural Networks with Both Time-Varying Delays and Continuously Distributed Delays

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Xiaohui Xu ◽  
Jiye Zhang ◽  
Quan Xu ◽  
Zilong Chen ◽  
Weifan Zheng
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Equilibrium Point ◽  
Global Exponential Stability ◽  
Dynamical Behavior ◽  
Sufficient Conditions ◽  
Distributed Delays ◽  
Time Varying ◽  
Homeomorphism Mapping ◽  
Complex Valued

This paper studies the global exponential stability for a class of impulsive disturbance complex-valued Cohen-Grossberg neural networks with both time-varying delays and continuously distributed delays. Firstly, the existence and uniqueness of the equilibrium point of the system are analyzed by using the corresponding property of M-matrix and the theorem of homeomorphism mapping. Secondly, the global exponential stability of the equilibrium point of the system is studied by applying the vector Lyapunov function method and the mathematical induction method. The established sufficient conditions show the effects of both delays and impulsive strength on the exponential convergence rate. The obtained results in this paper are with a lower level of conservatism in comparison with some existing ones. Finally, three numerical examples with simulation results are given to illustrate the correctness of the proposed results.

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