scholarly journals Exponential Convergence for Cellular Neural Networks with Time-Varying Delays in the Leakage Terms

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Zhibin Chen ◽  
Junxia Meng
Keyword(s):  
Neural Networks ◽  
Differential Inequality ◽  
Exponential Convergence ◽  
Zero Point ◽  
Functional Method ◽  
Cellular Neural Networks ◽  
Time Varying ◽  
All Solutions ◽  
Lyapunov Functional Method ◽  
Inequality Techniques

We consider a class of cellular neural networks with time-varying delays in the leakage terms. By applying Lyapunov functional method and differential inequality techniques, we establish new results to ensure that all solutions of the networks converge exponentially to zero point.

scholarly journals Periodic Solution for Impulsive Cellar Neural Networks with Time-Varying Delays in the Leakage Terms

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Bingwen Liu ◽  
Shuhua Gong
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Differential Inequality ◽  
Lyapunov Functional ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Time Varying ◽  
Activation Functions ◽  
Lyapunov Functional Method ◽  
Inequality Techniques

This paper is concerned with impulsive cellular neural networks with time-varying delays in leakage terms. Without assuming bounded and monotone conditions on activation functions, we establish sufficient conditions on existence and exponential stability of periodic solutions by using Lyapunov functional method and differential inequality techniques. Our results are complement to some recent ones.

The anti-periodic oscillations of shunting inhibitory cellular neural networks with time-varying delays and continuously distributed delays

2017 ◽  
Vol 10 (4) ◽  
pp. 513-529
Author(s):  
Changjin Xu ◽  
Peiluan Li
Keyword(s):  
Neural Networks ◽  
Periodic Solutions ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Cellular Neural Networks ◽  
Distributed Delays ◽  
Time Varying ◽  
Content Type ◽  
All Solutions ◽  
Inequality Technique

Purpose The purpose of this paper is to study the existence and exponential stability of anti-periodic solutions of a class of shunting inhibitory cellular neural networks (SICNNs) with time-varying delays and continuously distributed delays. Design/methodology/approach The inequality technique and Lyapunov functional method are applied. Findings Sufficient conditions are obtained to ensure that all solutions of the networks converge exponentially to the anti-periodic solution, which are new and complement previously known results. Originality/value There are few papers that deal with the anti-periodic solutions of delayed SICNNs with the form negative feedback – aij(t)αij(xij(t)).

Mean Square Asymptotic Stability of Neutral Stochastic Neutral Networks with Multiple Time-Varying Delays

2013 ◽  
Vol 684 ◽  
pp. 579-582
Author(s):  
Xiang Dong Shi
Keyword(s):  
Neural Networks ◽  
Asymptotic Stability ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Stochastic Neural Networks ◽  
Multiple Time ◽  
Time Varying ◽  
Lyapunov Functional Method ◽  
Inequality Techniques ◽  
Neutral Stochastic Neural Networks

The paper considers the problems of almost surely asymptotic stability for neutral stochastic neural networks with multiple time-varying delays. By applying Lyapunov functional method and differential inequality techniques, new sufficient conditions ensuring the existence and almost surely asymptotic stability of neutral stochastic neural networks with multiple time-varying delays are established. The results are shown to be generalizations of some previously published results and are less conservative than existing results.

Convergence of neutral type proportional-delayed HCNNs with D operators

2019 ◽  
Vol 12 (01) ◽  
pp. 1950002 ◽  
Author(s):  
Yanli Xu ◽  
Jiaming Zhong
Keyword(s):  
Neural Networks ◽  
Numerical Simulations ◽  
Differential Inequality ◽  
Exponential Convergence ◽  
Neutral Type ◽  
Cellular Neural Networks ◽  
High Order ◽  
Proportional Delays ◽  
Global Exponential Convergence ◽  
Inequality Techniques

This paper is concerned with neutral type high-order cellular neural networks (HCNNs) involving proportional delays and [Formula: see text] operators. Some criteria are established for the global exponential convergence of the addressed models by using differential inequality techniques. Moreover, an example and its numerical simulations are employed to illustrate the main results.

scholarly journals Almost Periodic Synchronization for Quaternion-Valued Neural Networks with Time-Varying Delays

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Yongkun Li ◽  
Xiaofang Meng ◽  
Yuan Ye
Keyword(s):  
Neural Networks ◽  
Differential Inequality ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Time Varying ◽  
Almost Periodic ◽  
Banach’S Fixed Point Theorem ◽  
Inequality Technique ◽  
Lyapunov Functional Method ◽  
Linear Differential

This paper focuses on the global exponential almost periodic synchronization of quaternion-valued neural networks with time-varying delays. By virtue of the exponential dichotomy of linear differential equations, Banach’s fixed point theorem, Lyapunov functional method, and differential inequality technique, some sufficient conditions are established for assuring the existence and global exponential synchronization of almost periodic solutions of the delayed quaternion-valued neural networks, which are completely new. Finally, we give one example with simulation to show the applicability and effectiveness of our main results.

scholarly journals Exponential Stability of BAM Fuzzy Cellular Neural Networks with Time-Varying Delays in Leakage Terms and Impulses

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Yongkun Li ◽  
Youqin Li
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Differential Inequality ◽  
Sufficient Conditions ◽  
Cellular Neural Networks ◽  
Time Varying ◽  
Fuzzy Cellular Neural Networks ◽  
Inequality Techniques ◽  
Theoretical Results

BAM fuzzy cellular neural networks with time-varying delays in leakage terms and impulses are considered. Some sufficient conditions for the exponential stability of the networks are established by using differential inequality techniques. The results of this paper are completely new and complementary to the previously known results. Finally, an example is given to demonstrate the effectiveness and conservativeness of our theoretical results.

scholarly journals Existence and exponential stability of a periodic solution for fuzzy cellular neural networks with time-varying delays

2011 ◽  
Vol 21 (4) ◽  
pp. 649-658 ◽  
Author(s):  
Qianhong Zhang ◽  
Lihui Yang ◽  
Daixi Liao
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Exponential Stability ◽  
Differential Inequality ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Cellular Neural Networks ◽  
Time Varying ◽  
Fuzzy Cellular Neural Networks ◽  
Inequality Technique

Existence and exponential stability of a periodic solution for fuzzy cellular neural networks with time-varying delays Fuzzy cellular neural networks with time-varying delays are considered. Some sufficient conditions for the existence and exponential stability of periodic solutions are obtained by using the continuation theorem based on the coincidence degree and the differential inequality technique. The sufficient conditions are easy to use in pattern recognition and automatic control. Finally, an example is given to show the feasibility and effectiveness of our methods.

scholarly journals Global Exponential Stability of Almost Periodic Solutions for SICNNs with Continuously Distributed Leakage Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Hong Zhang ◽  
Mingquan Yang
Keyword(s):  
Exponential Stability ◽  
Periodic Solutions ◽  
Differential Inequality ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Leakage Delays ◽  
Lyapunov Functional Method ◽  
Inequality Techniques

Shunting inhibitory cellular neural networks (SICNNs) are considered with the introduction of continuously distributed delays in the leakage (or forgetting) terms. By using the Lyapunov functional method and differential inequality techniques, some sufficient conditions for the existence and exponential stability of almost periodic solutions are established. Our results complement with some recent ones.

Finite-time synchronization for fuzzy inertial cellular neural networks with time-varying delays via integral inequality

2021 ◽  
pp. 1-14
Author(s):  
Zhenjie Wang ◽  
Wenxia Cui ◽  
Wenbin Jin
Keyword(s):  
Neural Networks ◽  
Integral Inequality ◽  
Finite Time ◽  
Time Synchronization ◽  
Cellular Neural Networks ◽  
Time Varying ◽  
Time Stability ◽  
Finite Time Stability ◽  
Synchronization Problem ◽  
Inequality Techniques

This paper mainly considers the finite-time synchronization problem of fuzzy inertial cellular neural networks (FICNNs) with time-varying delays. By constructing the suitable Lyapunov functional, and using integral inequality techniques, several sufficient criteria have been proposed to ensure the finite-time synchronization for the addressed (FICNNs). Without applying the known finite-time stability theorem, which is widely used to solve the finite-time synchronization problems for (FICNNs). In this paper, the proposed method is relatively convenient to solve finite-time synchronization problem of the addressed system, this paper extends the research works on the finite-time synchronization of (FICNNs). Finally, numerical simulations illustrated verify the effectiveness of the proposed results.

EXPONENTIAL CONVERGENCE OF CELLULAR NEURAL NETWORKS WITH CONTINUOUSLY DISTRIBUTED DELAYS

2007 ◽  
Vol 17 (12) ◽  
pp. 4403-4408
Author(s):  
BINGWEN LIU ◽  
ZHAOHUI YUAN
Keyword(s):  
Neural Networks ◽  
Periodic Function ◽  
Exponential Convergence ◽  
Sufficient Conditions ◽  
Cellular Neural Networks ◽  
Distributed Delays ◽  
Almost Periodic Function ◽  
Almost Periodic ◽  
Periodic Coefficients ◽  
All Solutions

In this paper the convergence behavior of delayed cellular neural networks without almost periodic coefficients are considered. Some sufficient conditions are established to ensure that all solutions of the networks converge exponentially to an almost periodic function, which are new, and also complement previously known results.

Sign in / Sign up

Export Citation Format

Share Document