Existence, uniqueness and global exponential stability of a periodic solution for a class of multidirectional associative memory neural network models

2014 ◽  
Vol 26 (4) ◽  
pp. 979-986 ◽  
Author(s):  
Yi Wang ◽  
Min Wang ◽  
Tiejun Zhou
Keyword(s):  
Neural Network ◽  
Periodic Solution ◽  
Exponential Stability ◽  
Associative Memory ◽  
Global Exponential Stability ◽  
Network Models ◽  
Neural Network Models

Global exponential periodicity and stability of neural network models with generalized piecewise constant delay

2021 ◽  
Vol 71 (2) ◽  
pp. 491-512
Author(s):  
Kuo-Shou Chiu ◽  
Fernando Córdova-Lepe
Keyword(s):  
Neural Network ◽  
Exponential Stability ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Network Models ◽  
Successive Approximations ◽  
Constant Delay ◽  
Neural Network Models ◽  
Piecewise Constant ◽  
Generalized Type

Abstract In this paper, the global exponential stability and periodicity are investigated for delayed neural network models with continuous coefficients and piecewise constant delay of generalized type. The sufficient condition for the existence and uniqueness of periodic solutions of the model is established by applying Banach’s fixed point theorem and the successive approximations method. By constructing suitable differential inequalities with generalized piecewise constant delay, some sufficient conditions for the global exponential stability of the model are obtained. Typical numerical examples with simulations are utilized to illustrate the validity and improvement in less conservatism of the theoretical results. This paper ends with a brief conclusion.

scholarly journals Existence and Global Exponential Stability of Equilibrium for Impulsive Cellular Neural Network Models with Piecewise Alternately Advanced and Retarded Argument

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Kuo-Shou Chiu
Keyword(s):  
Neural Network ◽  
Exponential Stability ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Network Models ◽  
Cellular Neural Network ◽  
Retarded Argument ◽  
Neural Network Models ◽  
Piecewise Constant Argument ◽  
Advanced Argument

We introduce impulsive cellular neural network models with piecewise alternately advanced and retarded argument (in short IDEPCA). The model with the advanced argument is system with strong anticipation. Some sufficient conditions are established for the existence and global exponential stability of a unique equilibrium. The approaches are based on employing Banach’s fixed point theorem and a new IDEPCA integral inequality of Gronwall type. The criteria given are easily verifiable, possess many adjustable parameters, and depend on impulses and piecewise constant argument deviations, which provides exibility for the design and analysis of cellular neural network models. Several numerical examples and simulations are also given to show the feasibility and effectiveness of our results.

scholarly journals Exponential stability in the Lagrange sense for Clifford-valued recurrent neural networks with time delays

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
G. Rajchakit ◽  
R. Sriraman ◽  
N. Boonsatit ◽  
P. Hammachukiattikul ◽  
C. P. Lim ◽  
...  
Keyword(s):  
Neural Network ◽  
Exponential Stability ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Network Models ◽  
Analytical Techniques ◽  
Lyapunov Stability Theory ◽  
Neural Network Models ◽  
Complex Valued ◽  
Clifford Numbers

AbstractThis paper considers the Clifford-valued recurrent neural network (RNN) models, as an augmentation of real-valued, complex-valued, and quaternion-valued neural network models, and investigates their global exponential stability in the Lagrange sense. In order to address the issue of non-commutative multiplication with respect to Clifford numbers, we divide the original n-dimensional Clifford-valued RNN model into $2^{m}n$ 2 m n real-valued models. On the basis of Lyapunov stability theory and some analytical techniques, several sufficient conditions are obtained for the considered Clifford-valued RNN models to achieve global exponential stability according to the Lagrange sense. Two examples are presented to illustrate the applicability of the main results, along with a discussion on the implications.

Existence and global exponential stability of equilibrium for impulsive neural network models with generalized piecewise constant delay

2021 ◽  
pp. 2250001
Author(s):  
Kuo-Shou Chiu
Keyword(s):  
Neural Network ◽  
Exponential Stability ◽  
Global Exponential Stability ◽  
Network Models ◽  
Cellular Neural Network ◽  
Impulsive Systems ◽  
Constant Delay ◽  
Neural Network Models ◽  
Piecewise Constant ◽  
Banach’S Fixed Point Theorem

In this paper, we investigate the models of the impulsive cellular neural network with generalized constant piecewise delay (IDEGPCD). To guarantee the existence, uniqueness and global exponential stability of the equilibrium state, several new adequate conditions are obtained, which extend the results of the previous literature. The method is based on utilizing Banach’s fixed point theorem and a new IDEGPCD’s Gronwall inequality. The criteria given are easy to check and when the impulsive effects do not affect, the results can be extracted from those of the non-impulsive systems. Typical numerical simulation examples are used to show the validity and effectiveness of the proposed results. We end the paper with a brief conclusion.

Sign in / Sign up

Export Citation Format

Share Document