Periodic solutions for stochastic Cohen–Grossberg neural networks with time-varying delays

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Wanqin Wu ◽  
Li Yang ◽  
Yaping Ren
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Exponential Stability ◽  
Fixed Points ◽  
Periodic Solutions ◽  
Sufficient Conditions ◽  
Stochastic Neural Networks ◽  
Time Varying ◽  
Deterministic Systems ◽  
Theoretical Results

AbstractThis paper is concerned with the periodic solutions for a class of stochastic Cohen–Grossberg neural networks with time-varying delays. Since there is a non-linearity in the leakage terms of stochastic Cohen–Grossberg neural networks, some techniques are needed to overcome the difficulty in dealing with the nonlinearity. By applying fixed points principle and Gronwall–Bellman inequality, some sufficient conditions on the existence and exponential stability of periodic solution for the stochastic neural networks are established. Moreover, a numerical example is presented to validate the theoretical results. Our results are also applicable to the existence and exponential stability of periodic solution for the corresponding deterministic systems.

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.

Exponential Stability for Stochastic Neural Networks with Time-Varying Delay and Leakage Delay

2015 ◽  
Vol 742 ◽  
pp. 399-403
Author(s):  
Ya Jun Li ◽  
Jing Zhao Li
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Sufficient Conditions ◽  
Leakage Delay ◽  
Linear Matrix ◽  
Stochastic Neural Networks ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Time Varying Delay ◽  
Varying Delay

This paper investigates the exponential stability problem for a class of stochastic neural networks with leakage delay. By employing a suitable Lyapunov functional and stochastic stability theory technic, the sufficient conditions which make the stochastic neural networks system exponential mean square stable are proposed and proved. All results are expressed in terms of linear matrix inequalities (LMIs). Example and simulation are presented to show the effectiveness of the proposed method.

scholarly journals Mean-Square Exponential Stability Analysis of Stochastic Neural Networks with Time-Varying Delays via Fixed Point Method

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Tianxiang Yao ◽  
Xianghong Lai
Keyword(s):  
Neural Networks ◽  
Fixed Point ◽  
Exponential Stability ◽  
Fixed Point Theory ◽  
Sufficient Conditions ◽  
Point Theory ◽  
Stability Study ◽  
Stochastic Neural Networks ◽  
Time Varying ◽  
Mean Square

This work addresses the stability study for stochastic cellular neural networks with time-varying delays. By utilizing the new research technique of the fixed point theory, we find some new and concise sufficient conditions ensuring the existence and uniqueness as well as mean-square global exponential stability of the solution. The presented algebraic stability criteria are easily checked and do not require the differentiability of delays. The paper is finally ended with an example to show the effectiveness of the obtained results.

scholarly journals Existence and Global Exponential Stability of Periodic Solutions for General Neural Networks with Time-Varying Delays

2008 ◽  
Vol 2008 ◽  
pp. 1-14 ◽  
Author(s):  
Xinsong Yang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Periodic Solutions ◽  
Differential Inequality ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Time Varying ◽  
Inequality Techniques ◽  
Coincidence Degree Theorem

By using the coincidence degree theorem and differential inequality techniques, sufficient conditions are obtained for the existence and global exponential stability of periodic solutions for general neural networks with time-varying (including bounded and unbounded) delays. Some known results are improved and some new results are obtained. An example is employed to illustrate our feasible results.

EXPONENTIAL STABILITY OF REACTION–DIFFUSION FUZZY RECURRENT NEURAL NETWORKS WITH TIME-VARYING DELAYS

2007 ◽  
Vol 17 (09) ◽  
pp. 3099-3108 ◽  
Author(s):  
QINGHUA ZHOU ◽  
LI WAN ◽  
JIANHUA SUN
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Recurrent Neural Networks ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Time Varying ◽  
Matrix Properties ◽  
Inequality Technique ◽  
Delay Dependent ◽  
Theoretical Results

Exponential stability of reaction–diffusion fuzzy recurrent neural networks (RDFRNNs) with time-varying delays are considered. By using the method of variational parameters, M-matrix properties and inequality technique, some delay-independent or delay-dependent sufficient conditions for guaranteeing the exponential stability of an equilibrium solution are obtained. One example is given to demonstrate the theoretical results.

scholarly journals Stability Analysis for Memristor-Based Complex-Valued Neural Networks with Time Delays

Entropy ◽  
2019 ◽  
Vol 21 (2) ◽  
pp. 120
Author(s):  
Ping Hou ◽  
Jun Hu ◽  
Jie Gao ◽  
Peican Zhu
Keyword(s):  
Numerical Simulation ◽  
Neural Networks ◽  
Stability Analysis ◽  
Exponential Stability ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Time Varying ◽  
Activation Functions ◽  
Complex Valued ◽  
Theoretical Results

In this paper, the problem of stability analysis for memristor-based complex-valued neural networks (MCVNNs) with time-varying delays is investigated extensively. This paper focuses on the exponential stability of the MCVNNs with time-varying delays. By means of the Brouwer’s fixed-point theorem and M-matrix, the existence, uniqueness, and exponential stability of the equilibrium point for MCVNNs are studied, and several sufficient conditions are obtained. In particular, these results can be applied to general MCVNNs whether the activation functions could be explicitly described by dividing into two parts of the real parts and imaginary parts or not. Two numerical simulation examples are provided to illustrate the effectiveness of the theoretical results.

scholarly journals Globalμ-Stability Analysis for Impulsive Stochastic Neural Networks with Unbounded Mixed Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-12
Author(s):  
Lizi Yin ◽  
Xinchun Wang
Keyword(s):  
Neural Networks ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Stochastic Neural Networks ◽  
Mixed Delays ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Software Packages ◽  
The Mean ◽  
Theoretical Results

We investigate the globalμ-stability in the mean square of impulsive stochastic neural networks with unbounded time-varying delays and continuous distributed delays. By choosing an appropriate Lyapunov-Krasovskii functional, a novel robust stability condition, in the form of linear matrix inequalities, is derived. These sufficient conditions can be tested by MATLAB LMI software packages. The results extend and improve the earlier publication. Two numerical examples are provided to illustrate the effectiveness of the obtained theoretical results.

Exponential Stability of Almost Periodic Solutions for Memristor-Based Neural Networks with Distributed Leakage Delays

2016 ◽  
Vol 28 (12) ◽  
pp. 2726-2756 ◽  
Author(s):  
Changjin Xu ◽  
Peiluan Li ◽  
Yicheng Pang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Periodic Solutions ◽  
Sufficient Conditions ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Leakage Delays ◽  
Lyapunov Function Method ◽  
Existence And Stability ◽  
Theoretical Results

In this letter, we deal with a class of memristor-based neural networks with distributed leakage delays. By applying a new Lyapunov function method, we obtain some sufficient conditions that ensure the existence, uniqueness, and global exponential stability of almost periodic solutions of neural networks. We apply the results of this solution to prove the existence and stability of periodic solutions for this delayed neural network with periodic coefficients. We then provide an example to illustrate the effectiveness of the theoretical results. Our results are completely new and complement the previous studies Chen, Zeng, and Jiang ( 2014 ) and Jiang, Zeng, and Chen ( 2015 ).

scholarly journals Periodic Solutions for Impulsive Stochastic BAM Neural Networks with Time-Varying Delays in Leakage Terms

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Li Yang ◽  
Yongkun Li
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Periodic Solutions ◽  
Integral Inequality ◽  
Sufficient Conditions ◽  
Time Varying ◽  
Bam Neural Networks

By using an integral inequality, we establish some sufficient conditions for the existence andp-exponential stability of periodic solutions for a class of impulsive stochastic BAM neural networks with time-varying delays in leakage terms. Moreover, we present an example to illustrate the feasibility of our results.

Periodic oscillation of memristor-based recurrent neural networks with time-varying delays and leakage delays

2018 ◽  
Vol 11 (3) ◽  
pp. 342-352
Author(s):  
Changjin Xu ◽  
Peiluan Li
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Exponential Stability ◽  
Recurrent Neural Networks ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Periodic Oscillation ◽  
Time Varying ◽  
Leakage Delays ◽  
Content Type

Purpose The purpose of this paper is to investigate the existence and global exponential stability of periodic solution of memristor-based recurrent neural networks with time-varying delays and leakage delays. Design/methodology/approach The differential inequality theory and some novel mathematical analysis techniques are applied. Findings A set of sufficient conditions which guarantee the existence and global exponential stability of periodic solution of involved model is derived. Practical implications It plays an important role in designing the neural networks. Originality/value The obtained results of this paper are new and complement some previous studies. The innovation of this paper concludes two aspects: the analysis on the existence and global exponential stability of periodic solution of memristor-based recurrent neural networks with time-varying delays and leakage delays is first proposed; and it is first time to establish the sufficient criterion which ensures the existence and global exponential stability of periodic solution of memristor-based recurrent neural networks with time-varying delays and leakage delays.

Sign in / Sign up

Export Citation Format

Share Document