scholarly journals Passivity Analysis of Coupled Stochastic Neural Networks with Multiweights

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Min Cao ◽  
Xun-Wu Yin ◽  
Wen-He Song ◽  
Xue-Mei Sun ◽  
Cheng-Dong Yang ◽  
...  
Keyword(s):  
Neural Networks ◽  
Stochastic Systems ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Stochastic Neural Networks ◽  
Analysis Techniques ◽  
Passivity Analysis ◽  
Input And Output ◽  
Lyapunov Functional Method ◽  
Theoretical Results

In this paper, we devote to the investigation of passivity in two types of coupled stochastic neural networks (CSNNs) with multiweights and incompatible input and output dimensions. First, some new definitions of passivity are proposed for stochastic systems that may have incompatible input and output dimensions. By utilizing stochastic analysis techniques and Lyapunov functional method, several sufficient conditions are respectively developed for ensuring that CSNNs without and with multiple delay couplings can realize passivity. Besides, the synchronization criteria for CSNNs with multiweights are established by employing the results of output-strictly passivity. Finally, two simulation examples are given to illustrate the validity of the theoretical results.

scholarly journals Square-Mean Pseudo Almost Periodic Solutions for Quaternion-Valued Stochastic Neural Networks with Time-Varying Delays

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Yuanyuan Hou ◽  
Lihua Dai
Keyword(s):  
Neural Networks ◽  
Stochastic Analysis ◽  
Stochastic Systems ◽  
Sufficient Conditions ◽  
Stochastic Neural Networks ◽  
Time Varying ◽  
Almost Periodic ◽  
Analysis Techniques ◽  
Pseudo Almost Periodic Solutions ◽  
Pseudo Almost Periodic

In this paper, we are concerned with a class of quaternion-valued stochastic neural networks with time-varying delays. Firstly, we cannot explicitly decompose the quaternion-valued stochastic systems into equivalent real-valued stochastic systems; by using the Banach fixed point theorem and stochastic analysis techniques, we obtain some sufficient conditions for the existence of square-mean pseudo almost periodic solutions for this class of neural networks. Then, by constructing an appropriate Lyapunov functional and stochastic analysis techniques, we can also obtain sufficient conditions for square-mean exponential stability of the considered neural networks. All of these results are new. Finally, two examples are given to illustrate the effectiveness and feasibility of our main 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.

scholarly journals Synchronization of Discrete-Time Stochastic Neural Networks with Random Delay

2011 ◽  
Vol 2011 ◽  
pp. 1-20 ◽  
Author(s):  
Haibo Bao ◽  
Jinde Cao
Keyword(s):  
Neural Networks ◽  
Time Delay ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Stochastic Neural Networks ◽  
Time Varying Delay ◽  
Random Delays ◽  
Random Fashion ◽  
Analysis Technique

By using a Lyapunov-Krasovskii functional method and the stochastic analysis technique, we investigate the problem of synchronization for discrete-time stochastic neural networks (DSNNs) with random delays. A control law is designed, and sufficient conditions are established that guarantee the synchronization of two identical DSNNs with random delays. Compared with the previous works, the time delay is assumed to be existent in a random fashion. The stochastic disturbances are described in terms of a Brownian motion and the time-varying delay is characterized by introducing a Bernoulli stochastic variable. Two examples are given to illustrate the effectiveness of the proposed results. The main contribution of this paper is that the obtained results are dependent on not only the bound but also the distribution probability of the time delay. Moreover, our results provide a larger allowance variation range of the delay, and are less conservative than the traditional delay-independent ones.

scholarly journals Exponential Stabilization of Coupled Hybrid Stochastic Delayed BAM Neural Networks: A Periodically Intermittent Control Method

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-14
Author(s):  
Yunjian Peng ◽  
Birong Zhao ◽  
Weijie Sun ◽  
Feiqi Deng
Keyword(s):  
Neural Networks ◽  
Closed Loop ◽  
Control Method ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Functional Method ◽  
Exponential Stabilization ◽  
Intermittent Control ◽  
Analysis Techniques ◽  
Basic Parameters

This paper considers exponential stabilization for a class of coupled hybrid stochastic delayed bidirectional associative memory neural networks (HSD-BAM-NN) with reaction-diffusion terms. A periodically intermittent controller is proposed to exponentially stabilize such an unstable HSD-BAM-NN, and sufficient conditions of the closed-loop BAM-NN system with exponential stabilization are derived by using Lyapunov-Krasovskii functional method, stochastic analysis techniques, and integral inequality property, which decide the basic parameters of the proposed controller. Furthermore, a framework to establish simulation algorithm with sampled states is presented to implement the stabilization controller. With a HSD-BAM-NN model of power synchronization in a photovoltaic (PV) array field, we illustrate numerical simulation results to verify the correctness and effectiveness of the proposed controller.

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 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 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 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 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 Analysis of Exponential Stability for Neutral Stochastic Cohen-Grossberg Neural Networks with Mixed Delays

2019 ◽  
Vol 2019 ◽  
pp. 1-15
Author(s):  
Tianqing Yang ◽  
Zuoliang Xiong ◽  
Cuiping Yang
Keyword(s):  
Neural Networks ◽  
Stochastic Analysis ◽  
Stability Problem ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Mixed Delays ◽  
Mean Square ◽  
Analysis Theory ◽  
The Mean ◽  
Theoretical Results

This paper is concerned with the mean-square exponential input-to-state stability problem for a class of stochastic Cohen-Grossberg neural networks. Different from prior works, neutral terms and mixed delays are discussed in our system. By employing the Lyapunov-Krasovskii functional method, Itô formula, Dynkin formula, and stochastic analysis theory, we obtain some novel sufficient conditions to ensure that the addressed system is mean-square exponentially input-to-state stable. Moreover, two numerical examples and their simulations are given to illustrate the correctness of the theoretical results.

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