scholarly journals Global Exponential Robust Stability of High-Order Hopfield Neural Networks with S-Type Distributed Time Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Haiyong Zheng ◽  
Bin Wu ◽  
Tengda Wei ◽  
Linshan Wang ◽  
Yangfan Wang
Keyword(s):  
Neural Networks ◽  
Robust Stability ◽  
Differential Inequality ◽  
Time Delays ◽  
Functional Method ◽  
High Order ◽  
Distributed Time Delays ◽  
Inequality Technique ◽  
Global Exponential Robust Stability ◽  
Lyapunov Functional Method

By employing differential inequality technique and Lyapunov functional method, some criteria of global exponential robust stability for the high-order neural networks with S-type distributed time delays are established, which are easy to be verified with a wider adaptive scope.

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 LMI-Based Approach for Exponential Robust Stability of High-Order Hopfield Neural Networks with Time-Varying Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Yangfan Wang ◽  
Linshan Wang
Keyword(s):  
Neural Networks ◽  
Linear Matrix Inequality ◽  
Robust Stability ◽  
High Order ◽  
Hopfield Neural Networks ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Global Exponential Robust Stability

This paper studies the problems of global exponential robust stability of high-order hopfield neural networks with time-varying delays. By employing a new Lyapunov-Krasovskii functional and linear matrix inequality, some criteria of global exponential robust stability for the high-order neural networks are established, which are easily verifiable and have a wider adaptive.

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.

scholarly journals Dynamical Analysis for High-Order Delayed Hopfield Neural Networks with Impulses

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Dengwang Li
Keyword(s):  
Neural Networks ◽  
Functional Method ◽  
High Order ◽  
Hopfield Neural Networks ◽  
Dynamical Analysis ◽  
Linear Matrix ◽  
Stability Criteria ◽  
Linear Matrix Inequality Approach ◽  
Lyapunov Functional Method

The global exponential stability and uniform stability of the equilibrium point for high-order delayed Hopfield neural networks with impulses are studied. By utilizing Lyapunov functional method, the quality of negative definite matrix, and the linear matrix inequality approach, some new stability criteria for such system are derived. The results are related to the size of delays and impulses. Two examples are also given to illustrate the effectiveness of our results.

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 New Results for Periodic Solution of High-Order BAM Neural Networks with Continuously Distributed Delays and Impulses

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
Chang-Bo Yang ◽  
Ting-Zhu Huang ◽  
Jin-Liang Shao
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Matrix Theory ◽  
Sufficient Conditions ◽  
Functional Method ◽  
High Order ◽  
Distributed Delays ◽  
Bam Neural Networks ◽  
New Type ◽  
Lyapunov Functional Method

ByM-matrix theory, inequality techniques, and Lyapunov functional method, certain sufficient conditions are obtained to ensure the existence, uniqueness, and global exponential stability of periodic solution for a new type of high-order BAM neural networks with continuously distributed delays and impulses. These novel conditions extend and improve some previously known results in the literature. Finally, an illustrative example and its numerical simulation are given to show the feasibility and correctness of the derived criteria.

scholarly journals Novel Criteria on Global Robust Exponential Stability to a Class of Reaction-Diffusion Neural Networks with Delays

2009 ◽  
Vol 2009 ◽  
pp. 1-14 ◽  
Author(s):  
Jie Pan ◽  
Shouming Zhong
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Robust Stability ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Functional Method ◽  
Compact Sets ◽  
Robust Exponential Stability ◽  
Delayed Neural Networks ◽  
Global Exponential Robust Stability

The global exponential robust stability is investigated to a class of reaction-diffusion Cohen-Grossberg neural network (CGNNs) with constant time-delays, this neural network contains time invariant uncertain parameters whose values are unknown but bounded in given compact sets. By employing the Lyapunov-functional method, several new sufficient conditions are obtained to ensure the global exponential robust stability of equilibrium point for the reaction diffusion CGNN with delays. These sufficient conditions depend on the reaction-diffusion terms, which is a preeminent feature that distinguishes the present research from the previous research on delayed neural networks with reaction-diffusion. Two examples are given to show the effectiveness of the obtained results.

scholarly journals Anti-periodic solutions for fractional-order bidirectional associative memory neural networks with delays

2019 ◽  
Vol 23 (Suppl. 6) ◽  
pp. 2169-2177
Author(s):  
Munevver Tuz ◽  
Gulden Suroglu
Keyword(s):  
Neural Networks ◽  
Periodic Solutions ◽  
Fractional Order ◽  
Associative Memory ◽  
Lyapunov Functional ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Bidirectional Associative Memory ◽  
Inequality Technique ◽  
Lyapunov Functional Method

This paper concerns fractional-order bidirectional associative memory neural networks with distributed delays. Based on inequality technique and Lyapunov functional method, some novel sufficient conditions are obtained for the existence and exponential stability of anti-periodic solutions are established. An example is given to show the feasibility main results.

EXPONENTIAL SYNCHRONIZATION IN DRIVE-RESPONSE SYSTEMS OF HOPFIELD-TYPE NEURAL NETWORKS WITH TIME DELAYS

2007 ◽  
Vol 17 (11) ◽  
pp. 4167-4176 ◽  
Author(s):  
CHUN-HSIEN LI ◽  
SUH-YUH YANG
Keyword(s):  
Neural Networks ◽  
Time Delays ◽  
Functional Method ◽  
Exponential Synchronization ◽  
Weighted Sum ◽  
Response Type ◽  
Response Systems ◽  
Coupling Strengths ◽  
Lyapunov Functional Method ◽  
Exponential Rates

In this paper we investigate the drive-response type synchronization of Hopfield-type neural networks with connection time delays for both discrete and distributed cases. By employing the Lyapunov functional method, we propose a sufficient condition to ensure the occurrence of synchronization with exponential rates. This criterion is independent of time delays as well as the types of delay. We prove that the exponential synchronization occurs provided a certain weighted sum of the connection and coupling strengths is negative enough, no matter that the connection time delay is of discrete or distributed case. Numerical examples are provided to illustrate the results.

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