EXISTENCE ANALYSIS OF MOSAIC SOLUTIONS FOR ONE-DIMENSIONAL CELLULAR NEURAL NETWORKS

2006 ◽  
Vol 16 (12) ◽  
pp. 3669-3677 ◽  
Author(s):  
YUN-QUAN KE ◽  
FENG-YAN ZHOU
Keyword(s):  
Neural Networks ◽  
Sufficient Conditions ◽  
Cellular Neural Networks ◽  
One Dimensional

In this letter, the mosaic solutions of one-dimensional Cellular Neural Networks system (CNNs) are investigated. Three types of parameters, the synaptic weights, the input terms and the threshold are properly chosen in terms of Chua's driving-point plot. Moreover, we give sufficient conditions for the existence of the mosaic solutions.

SNAP-BACK REPELLERS AND CHAOTIC TRAVELING WAVES IN ONE-DIMENSIONAL CELLULAR NEURAL NETWORKS

2007 ◽  
Vol 17 (06) ◽  
pp. 1969-1983 ◽  
Author(s):  
YA-WEN CHANG ◽  
JONQ JUANG ◽  
CHIN-LUNG LI
Keyword(s):  
Neural Networks ◽  
Fixed Point ◽  
Discrete Time ◽  
Traveling Waves ◽  
Sufficient Conditions ◽  
Cellular Neural Networks ◽  
One Dimensional ◽  
Time Analogy

In 1998, Chen et al. [1998] found an error in Marotto's paper [1978]. It was pointed out by them that the existence of an expanding fixed point z of a map F in Br( z ), the ball of radius r with center at z does not necessarily imply that F is expanding in Br( z ). Subsequent efforts (see e.g. [Chen et al., 1998; Lin et al., 2002; Li & Chen, 2003]) in fixing the problems have some discrepancies since they only give conditions for which F is expanding "locally". In this paper, we give sufficient conditions so that F is "globally" expanding. This, in turn, gives more satisfying definitions of a snap-back repeller. We then use those results to show the existence of chaotic backward traveling waves in a discrete time analogy of one-dimensional Cellular Neural Networks (CNNs). Some computer evidence of chaotic traveling waves is also given.

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.

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.

scholarly journals Exponential Stability and Periodicity of Fuzzy Delayed Reaction-Diffusion Cellular Neural Networks with Impulsive Effect

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Guowei Yang ◽  
Yonggui Kao ◽  
Changhong Wang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Matrix Theory ◽  
Sufficient Conditions ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Cellular Neural Networks ◽  
Impulsive Effect ◽  
Time Varying ◽  
Delayed Reaction

This paper considers dynamical behaviors of a class of fuzzy impulsive reaction-diffusion delayed cellular neural networks (FIRDDCNNs) with time-varying periodic self-inhibitions, interconnection weights, and inputs. By using delay differential inequality,M-matrix theory, and analytic methods, some new sufficient conditions ensuring global exponential stability of the periodic FIRDDCNN model with Neumann boundary conditions are established, and the exponential convergence rate index is estimated. The differentiability of the time-varying delays is not needed. An example is presented to demonstrate the efficiency and effectiveness of the obtained results.

EXPONENTIAL STABILITY ANALYSIS OF NEURAL NETWORKS WITH VARIABLE DELAYS

2010 ◽  
Vol 20 (05) ◽  
pp. 1541-1549 ◽  
Author(s):  
MAN-CHUN TAN ◽  
YAN ZHANG ◽  
WEN-LI SU ◽  
YU-NONG ZHANG
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Exponential Stability ◽  
Equilibrium Point ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Cellular Neural Networks ◽  
Variable Delays

Some sufficient conditions to ensure the existence, uniqueness and global exponential stability of the equilibrium point of cellular neural networks with variable delays are derived. These results extend and improve the existing ones in the literature. Two illustrative examples are given to demonstrate the effectiveness of our results.

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.

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