Exponential Stability and Periodic Solutions of Impulsive Neural Network Models with Piecewise Constant Argument

2017 ◽  
Vol 151 (1) ◽  
pp. 199-226 ◽  
Author(s):  
Kuo-Shou Chiu
Keyword(s):  
Neural Network ◽  
Exponential Stability ◽  
Periodic Solutions ◽  
Network Models ◽  
Neural Network Models ◽  
Piecewise Constant ◽  
Piecewise Constant Argument ◽  
Constant Argument

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.

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.

scholarly journals Existence and Uniqueness of Periodic Solutions for a Second-Order Nonlinear Differential Equation with Piecewise Constant Argument

2009 ◽  
Vol 2009 ◽  
pp. 1-14 ◽  
Author(s):  
Gen-qiang Wang ◽  
Sui Sun Cheng
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Periodic Solutions ◽  
Nonlinear Differential Equation ◽  
Existence And Uniqueness ◽  
Second Order ◽  
Piecewise Constant ◽  
Piecewise Constant Argument ◽  
Order Nonlinear Differential Equation ◽  
Constant Argument

Based on a continuation theorem of Mawhin, a unique periodic solution is found for a second-order nonlinear differential equation with piecewise constant argument.

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