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

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.

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Exponential Stability of Periodic Solution to Wilson-Cowan Networks with Time-Varying Delays on Time Scales

Advances in Artificial Neural Systems ◽

10.1155/2014/750532 ◽

2014 ◽

Vol 2014 ◽

pp. 1-10

Author(s):

Jinxiang Cai ◽

Zhenkun Huang ◽

Honghua Bin

Keyword(s):

Periodic Solution ◽

Stability Analysis ◽

Exponential Stability ◽

Time Scales ◽

Continuous Time ◽

Lyapunov Functional ◽

Contraction Mapping ◽

Sufficient Conditions ◽

Contraction Mapping Principle ◽

Time Varying

We present stability analysis of delayed Wilson-Cowan networks on time scales. By applying the theory of calculus on time scales, the contraction mapping principle, and Lyapunov functional, new sufficient conditions are obtained to ensure the existence and exponential stability of periodic solution to the considered system. The obtained results are general and can be applied to discrete-time or continuous-time Wilson-Cowan networks.

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

Abstract and Applied Analysis ◽

10.1155/2013/307981 ◽

2013 ◽

Vol 2013 ◽

pp. 1-14 ◽

Cited By ~ 6

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.

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

Abstract and Applied Analysis ◽

10.1155/2013/701087 ◽

2013 ◽

Vol 2013 ◽

pp. 1-10 ◽

Cited By ~ 3

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.

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Periodic solution for inertial neural networks with variable parameters

AIMS Mathematics ◽

10.3934/math.2021789 ◽

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>

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A Novel Stability Analysis of Uncertain Switched Systems with Time-Varying Delays

Journal of Control Science and Engineering ◽

10.1155/2015/745175 ◽

2015 ◽

Vol 2015 ◽

pp. 1-7 ◽

Cited By ~ 3

Author(s):

Ganji Huang ◽

Shixian Luo ◽

Linna Wei ◽

Wuhua Chen

Keyword(s):

Switched Systems ◽

Lyapunov Functional ◽

Sufficient Conditions ◽

Functional Method ◽

Time Varying ◽

System Parameters ◽

Time Varying Delay ◽

Lyapunov Functional Method ◽

The Stability ◽

Varying Delay

This paper deals with the stability of switched systems with time-varying delay. The time-varying system parameters are assumed to be norm-bounded. Based on a novel switched time-varying Lyapunov functional method, some new LMI-based sufficient conditions have been obtained to ensure the exponential stability for the uncertain switched delays systems. Finally, the proposed method is applied to a numerical example and the simulative results are also given.

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Existence and stability of anti-periodic solutions for impulsive fuzzy Cohen-Grossberge neural networks on time scales

Mathematica Slovaca ◽

10.2478/s12175-013-0191-5 ◽

2014 ◽

Vol 64 (1) ◽

Author(s):

Qianhong Zhang ◽

Lihui Yang ◽

Jingzhong Liu

Keyword(s):

Neural Networks ◽

Exponential Stability ◽

Periodic Solutions ◽

Time Scales ◽

Lyapunov Functional ◽

Global Exponential Stability ◽

Sufficient Conditions ◽

Coincidence Degree ◽

Existence And Stability

AbstractBy applying the method of coincidence degree and constructing suitable Lyapunov functional, some sufficient conditions are established for the existence and global exponential stability of anti-periodic solutions for a kind of impulsive fuzzy Cohen-Grossberg neural networks on time scales. Moreover an example is given to illustrate our results.

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Stability Analysis of Static Neural Network with Time-Varying Delays

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.644-650.2442 ◽

2014 ◽

Vol 644-650 ◽

pp. 2442-2445

Author(s):

Rui Zhang ◽

Meng Xin Li ◽

Mei Ju Liu

Keyword(s):

Exponential Stability ◽

Lyapunov Functional ◽

Global Exponential Stability ◽

Functional Method ◽

Linear Matrix ◽

Time Varying ◽

Matrix Inequalities ◽

Main Condition ◽

Change Rate ◽

Lyapunov Functional Method

In this paper, the global exponential stability is discussed for static neural networks with time varying delays. On the basis of the linear matrix inequalities (LMIs) technique, and Lyapunov functional method, we have obtained the main condition to ensure the global exponential stability of the equilibrium point for this system, which is dependent on the change rate of time varying delays. The proposed result is less restrictive than those given in the earlier literatures, easier to check in practice. Remarks are made with other previous works to show the superiority of the obtained results, and the simulation examples are used to demonstrate the effectiveness of our results.

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Existence and Stability of Periodic Solutions for Impulsive Fuzzy Cohen-Grossberg Neural Networks on Time Scales

Annals of the Alexandru Ioan Cuza University - Mathematics ◽

10.1515/aicu-2015-0024 ◽

2015 ◽

Vol 0 (0) ◽

Author(s):

Qianhong Zhang ◽

Jingzhong Liu ◽

Yuanfu Shao

Keyword(s):

Neural Networks ◽

Exponential Stability ◽

Periodic Solutions ◽

Time Scales ◽

Lyapunov Functional ◽

Sufficient Conditions ◽

Coincidence Degree ◽

Globally Exponential Stability ◽

Existence And Stability

Abstract By applying the method of coincidence degree and constructing a suitable Lyapunov functional, some sufficient conditions are established for the existence and globally exponential stability of periodic solutions for a kind of impulsive fuzzy Cohen- Grossberg neural networks on time scales. Moreover an example is given to illustrate our results.

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Stability and Passivity of Spatially and Temporally Complex Dynamical Networks with Time-Varying Delays

Mathematical Problems in Engineering ◽

10.1155/2014/412169 ◽

2014 ◽

Vol 2014 ◽

pp. 1-8 ◽

Cited By ~ 1

Author(s):

Shun-Yan Ren ◽

Yue-Hui Zhao

Keyword(s):

Exponential Stability ◽

Numerical Simulations ◽

Lyapunov Functional ◽

Global Exponential Stability ◽

Functional Method ◽

Time Varying ◽

Complex Dynamical Network ◽

Input And Output ◽

Lyapunov Functional Method ◽

Inequality Techniques

This paper proposes a new complex dynamical network model, in which the state, input, and output variables are varied with the time and space variables. By utilizing the Lyapunov functional method combined with the inequality techniques, several criteria for passivity and global exponential stability are established. Finally, numerical simulations are given to illustrate the effectiveness of the obtained results.

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

Thermal Science ◽

10.2298/tsci190805406t ◽

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.

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