Associative Memories Based on Discrete-Time Cellular Neural Networks with One-Dimensional Space-Invariant Templates

2006 ◽  
pp. 824-829
Author(s):  
Zhigang Zeng ◽  
Jun Wang
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Dimensional Space ◽  
Cellular Neural Networks ◽  
Associative Memories ◽  
One Dimensional

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.

DISCRETE-TIME CELLULAR NEURAL NETWORKS FOR ASSOCIATIVE MEMORIES WITH APPLICATION TO PATTERN CLASSIFICATION

2003 ◽  
Vol 12 (04) ◽  
pp. 491-503
Author(s):  
GIUSEPPE GRASSI
Keyword(s):  
Neural Networks ◽  
Pattern Classification ◽  
Discrete Time ◽  
Initial Conditions ◽  
Design Method ◽  
Cellular Neural Networks ◽  
Design Tool ◽  
Circulant Matrices ◽  
Stable Equilibrium Point ◽  
Associative Memories

This paper focuses on Discrete-Time Cellular Neural Networks (DTCNNs) for associative memories with application to pattern classification. At first, DTCNNs with a globally asymptotically stable equilibrium point are designed to behave as associative memories. The objective is achieved by considering feedback parameters related to circulant matrices and by satisfying frequency domain stability criteria. The approach, by generating DTCNNs where the input data are fed via external inputs rather than initial conditions, enables both hetero-associative and auto-associative memories to be designed. Numerical examples are reported in order to show the capabilities of the design tool. Successively, an application of DTCNNs to pattern classification is illustrated. Namely, it is shown that patterns belonging to the training set as well as patterns outside it can be reliably classified using the proposed design method. Comparisons with well-established classification techniques, such as signature technique and modified Fourier descriptor technique, clearly highlight the performances of the approach developed herein.

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