The anti-periodic oscillations of shunting inhibitory cellular neural networks with time-varying delays and continuously distributed delays

2017 ◽  
Vol 10 (4) ◽  
pp. 513-529
Author(s):  
Changjin Xu ◽  
Peiluan Li
Keyword(s):  
Neural Networks ◽  
Periodic Solutions ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Cellular Neural Networks ◽  
Distributed Delays ◽  
Time Varying ◽  
Content Type ◽  
All Solutions ◽  
Inequality Technique

Purpose The purpose of this paper is to study the existence and exponential stability of anti-periodic solutions of a class of shunting inhibitory cellular neural networks (SICNNs) with time-varying delays and continuously distributed delays. Design/methodology/approach The inequality technique and Lyapunov functional method are applied. Findings Sufficient conditions are obtained to ensure that all solutions of the networks converge exponentially to the anti-periodic solution, which are new and complement previously known results. Originality/value There are few papers that deal with the anti-periodic solutions of delayed SICNNs with the form negative feedback – aij(t)αij(xij(t)).

EXPONENTIAL CONVERGENCE BEHAVIOR OF FUZZY CELLULAR NEURAL NETWORKS WITH DISTRIBUTED DELAYS AND TIME-VARYING COEFFICIENTS

2009 ◽  
Vol 19 (07) ◽  
pp. 2455-2462 ◽  
Author(s):  
MAN-CHUN TAN
Keyword(s):  
Neural Networks ◽  
Sufficient Conditions ◽  
Cellular Neural Networks ◽  
Distributed Delays ◽  
Time Varying ◽  
Fuzzy Cellular Neural Networks ◽  
Lipschitz Continuous ◽  
Varying Coefficients ◽  
All Solutions ◽  
Time Varying Coefficients

In this paper, a class of fuzzy cellular neural networks (FCNNs) with distributed delays and time-varying coefficients is studied. By employing the mathematical analysis method, some sufficient conditions are derived for ensuring that all solutions of such FCNNs converge exponentially to zero. Both the Lipschitz continuous condition on activation functions and the differentiability of time-varying delays are not required in this study.

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 CONVERGENCE OF CELLULAR NEURAL NETWORKS WITH CONTINUOUSLY DISTRIBUTED DELAYS

2007 ◽  
Vol 17 (12) ◽  
pp. 4403-4408
Author(s):  
BINGWEN LIU ◽  
ZHAOHUI YUAN
Keyword(s):  
Neural Networks ◽  
Periodic Function ◽  
Exponential Convergence ◽  
Sufficient Conditions ◽  
Cellular Neural Networks ◽  
Distributed Delays ◽  
Almost Periodic Function ◽  
Almost Periodic ◽  
Periodic Coefficients ◽  
All Solutions

In this paper the convergence behavior of delayed cellular neural networks without almost periodic coefficients are considered. Some sufficient conditions are established to ensure that all solutions of the networks converge exponentially to an almost periodic function, which are new, and also complement previously known results.

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 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 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 Periodic Solutions for Shunting Inhibitory Cellular Neural Networks of Neutral Type with Time-Varying Delays in the Leakage Term on Time Scales

2014 ◽  
Vol 2014 ◽  
pp. 1-16 ◽  
Author(s):  
Yongkun Li ◽  
Lei Wang ◽  
Yu Fei
Keyword(s):  
Neural Networks ◽  
Periodic Solutions ◽  
Time Scales ◽  
Fixed Point Theorems ◽  
Neutral Type ◽  
Sufficient Conditions ◽  
Cellular Neural Networks ◽  
Time Varying ◽  
Leakage Term ◽  
Linear Dynamic

A class of shunting inhibitory cellular neural networks of neutral type with time-varying delays in the leakage term on time scales is proposed. Based on the exponential dichotomy of linear dynamic equations on time scales, fixed point theorems, and calculus on time scales we obtain some sufficient conditions for the existence and global exponential stability of periodic solutions for that class of neural networks. The results of this paper are completely new and complementary to the previously known results even if the time scale𝕋=ℝorℤ. Moreover, we present illustrative numerical examples to show the feasibility of our results.

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