A study on limit cycles in nearly symmetric cellular neural networks

2003 ◽  
Author(s):  
M. Di Marco ◽  
M. Forti ◽  
A. Tesi
Keyword(s):  
Neural Networks ◽  
Limit Cycles ◽  
Cellular Neural Networks

CHAOS AND TWO-TORI IN A NEW FAMILY OF 4-CNNS

2007 ◽  
Vol 17 (03) ◽  
pp. 953-963 ◽  
Author(s):  
XIAO-SONG YANG ◽  
YAN HUANG
Keyword(s):  
Neural Networks ◽  
Limit Cycle ◽  
Limit Cycles ◽  
Cellular Neural Networks ◽  
Lyapunov Spectrum ◽  
Regular Array ◽  
Poincaré Maps ◽  
One Dimensional ◽  
Poincare Maps ◽  
New Family

In this paper we demonstrate chaos, two-tori and limit cycles in a new family of Cellular Neural Networks which is a one-dimensional regular array of four cells. The Lyapunov spectrum is calculated in a range of parameters, the bifurcation plots are presented as well. Furthermore, we confirm the nature of limit cycle, chaos and two-tori by studying Poincaré maps.

STRUCTURALLY STABLE TWO-CELL CELLULAR NEURAL NETWORKS

2004 ◽  
Vol 14 (08) ◽  
pp. 2579-2653 ◽  
Author(s):  
MAKOTO ITOH ◽  
LEON O. CHUA
Keyword(s):  
Neural Networks ◽  
Phase Portrait ◽  
Limit Cycles ◽  
Equilibrium Points ◽  
Cellular Neural Networks ◽  
Global Phase Portrait ◽  
Structurally Stable

The global phase portrait of structurally stable two-cell cellular neural networks is studied. The configuration of equilibrium points, the number of limit cycles and their locations are investigated systematically.

New Criteria on Stability of Dynamic Memristor Delayed Cellular Neural Networks

2020 ◽  
pp. 1-13
Author(s):  
Kun Deng ◽  
Song Zhu ◽  
Wei Dai ◽  
Chunyu Yang ◽  
Shiping Wen
Keyword(s):  
Neural Networks ◽  
Cellular Neural Networks ◽  
New Criteria

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.

scholarly journals An LMI Approach for Dynamics of Switched Cellular Neural Networks with Mixed Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Chuangxia Huang ◽  
Hanfeng Kuang ◽  
Xiaohong Chen ◽  
Fenghua Wen
Keyword(s):  
Neural Networks ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Cellular Neural Networks ◽  
Linear Matrix ◽  
Mixed Delays ◽  
Ultimate Boundedness ◽  
Globally Exponential Stability ◽  
Average Dwell Time Method ◽  
Uniformly Ultimate Boundedness

This paper considers the dynamics of switched cellular neural networks (CNNs) with mixed delays. With the help of the Lyapnnov function combined with the average dwell time method and linear matrix inequalities (LMIs) technique, some novel sufficient conditions on the issue of the uniformly ultimate boundedness, the existence of an attractor, and the globally exponential stability for CNN are given. The provided conditions are expressed in terms of LMI, which can be easily checked by the effective LMI toolbox in Matlab in practice.

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