scholarly journals Periodic solution for inertial neural networks with variable parameters

2021 ◽  
Vol 6 (12) ◽  
pp. 13580-13591
Author(s):  
Lingping Zhang ◽  
◽  
Bo Du
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Asymptotic Stability ◽  
Lyapunov Functional ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Mawhin’S Continuation Theorem ◽  
Variable Parameters ◽  
Inertial Neural Networks ◽  
Lyapunov Functional Method

<abstract><p>We discuss periodic solution problems and asymptotic stability for inertial neural networks with $ D- $operator and variable parameters. Based on Mawhin's continuation theorem and Lyapunov functional method, some new sufficient conditions on the existence and asymptotic stability of periodic solutions are established. Finally, a numerical example verifies the effectiveness of the obtained results.</p></abstract>

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 Periodic solution for neutral-type inertial neural networks with time-varying delays

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Mei Xu ◽  
Bo Du
Keyword(s):  
Neural Networks ◽  
Lyapunov Functional ◽  
Neutral Type ◽  
Functional Method ◽  
Time Varying ◽  
Mawhin’S Continuation Theorem ◽  
Existence And Stability ◽  
Inertial Neural Networks ◽  
Lyapunov Functional Method ◽  
Theoretical Results

Abstract In this paper the problems of the existence and stability of periodic solutions of neutral-type inertial neural networks with time-varying delays are discussed by applying Mawhin’s continuation theorem and Lyapunov functional method. Finally, two numerical examples are given to illustrate our theoretical results.

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.

The Globally Asymptotic Stability Analysis of the Delayed Recurrent Neural Networks Stability Criterion via LMI Technique and Nonsmooth Analysis

2013 ◽  
Vol 380-384 ◽  
pp. 2030-2033
Author(s):  
Zhen Cai Li ◽  
Yang Wang
Keyword(s):  
Neural Networks ◽  
Asymptotic Stability ◽  
Recurrent Neural Networks ◽  
Nonsmooth Analysis ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Linear Matrix ◽  
Time Varying ◽  
Globally Asymptotic Stability ◽  
Lyapunov Functional Method

This paper considers the problem of globally asymptotic stability of the recurrent neural networks with time-varying delays. A linear matrix inequality (LMI) technology and Lyapunov functional method is employed by combing the means of the nonsmooth analysis. A few new sufficient conditions and criterions were proposed to ensure the delayed recurrent neural networks are uniqueness and globally asymptotic stability of their equilibrium point. A few simulation examples are presented to demonstrate the effectiveness of the results and to improve feasibility.

scholarly journals Positive periodic solution for inertial neural networks with time-varying delays

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Feng Duan ◽  
Bo Du
Keyword(s):  
Neural Networks ◽  
Periodic Solutions ◽  
Sufficient Conditions ◽  
Positive Periodic Solution ◽  
Functional Method ◽  
Time Varying ◽  
Positive Periodic Solutions ◽  
Mawhin’S Continuation Theorem ◽  
Existence And Stability ◽  
Inertial Neural Networks

AbstractIn this paper the problems of the existence and stability of positive periodic solutions of inertial neural networks with time-varying delays are discussed by the use of Mawhin’s continuation theorem and Lyapunov functional method. Some sufficient conditions are obtained for guaranteeing the existence and stability of positive periodic solutions of the considered system. Finally, a numerical example is given to illustrate the effectiveness of the obtained results.

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 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.

Stabilization for a class of delayed switched inertial neural networks via non-reduced order method

2021 ◽  
pp. 014233122098594
Author(s):  
Xuan Chen ◽  
Dongyun Lin
Keyword(s):  
Neural Networks ◽  
Comparative Research ◽  
Lyapunov Functional ◽  
Sufficient Conditions ◽  
Global Stabilization ◽  
Order Method ◽  
Reduced Order ◽  
Global Asymptotic Stabilization ◽  
Inertial Neural Networks ◽  
Barbalat Lemma

This paper tackles the issue of global stabilization for a class of delayed switched inertial neural networks (SINN). Distinct from the frequently employed reduced-order technique, this paper studies SINN directly through non-reduced order method. By constructing a novel Lyapunov functional and using Barbalat Lemma, sufficient conditions for the global asymptotic stabilization issue and global exponential stabilization issue of the considered SINN are established. Numerical simulations further confirm the feasibility of the main results. The comparative research shows that global stabilization results of this paper complement and improve some existing work.

scholarly journals Global Exponential Stability of Learning-Based Fuzzy Networks on Time Scales

2015 ◽  
Vol 2015 ◽  
pp. 1-15
Author(s):  
Juan Chen ◽  
Zhenkun Huang ◽  
Jinxiang Cai
Keyword(s):  
Exponential Stability ◽  
Time Scales ◽  
Continuous Time ◽  
Lyapunov Functional ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Fuzzy Neural Networks ◽  
New Learning ◽  
Fuzzy Neural ◽  
Lyapunov Functional Method

We investigate a class of fuzzy neural networks with Hebbian-type unsupervised learning on time scales. By using Lyapunov functional method, some new sufficient conditions are derived to ensure learning dynamics and exponential stability of fuzzy networks on time scales. Our results are general and can include continuous-time learning-based fuzzy networks and corresponding discrete-time analogues. Moreover, our results reveal some new learning behavior of fuzzy synapses on time scales which are seldom discussed in the literature.

scholarly journals Dynamics of Cohen-Grossberg Neural Networks with Mixed Delays and Impulses

2008 ◽  
Vol 2008 ◽  
pp. 1-14 ◽  
Author(s):  
Xinsong Yang ◽  
Chuangxia Huang ◽  
Defei Zhang ◽  
Yao Long
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Inequality ◽  
Lyapunov Functional ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Mixed Delays ◽  
Inequality Techniques

Impulsive Cohen-Grossberg neural networks with bounded and unbounded delays (i.e., mixed delays) are investigated. By using the Leray-Schauder fixed point theorem, differential inequality techniques, and constructing suitable Lyapunov functional, several new sufficient conditions on the existence and global exponential stability of periodic solution for the system are obtained, which improves some of the known results. An example and its numerical simulations are employed to illustrate our feasible results.

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