ON THE MONOTONICITY OF ENTROPY FOR MULTILAYER CELLULAR NEURAL NETWORKS

2009 ◽  
Vol 19 (11) ◽  
pp. 3657-3670 ◽  
Author(s):  
JUNG-CHAO BAN ◽  
CHIH-HUNG CHANG
Keyword(s):  
Dynamical System ◽  
Neural Networks ◽  
Topological Entropy ◽  
Cellular Neural Networks ◽  
Strict Monotonicity ◽  
One Dimensional ◽  
Number Of Layers ◽  
Nested Sequence

This work investigates the monotonicity of topological entropy for one-dimensional multilayer cellular neural networks. The interacting radius and number of layers are treated as parameters. Fix either one of them; the set of topological entropies grows as a strictly nested sequence with respect to one another. Apart from the comparison of the set of topological entropies, maximal and minimal templates are indicators of a dynamical system. Our results demonstrate that maximal and minimal templates of larger interacting radius (respectively number of layers) dominate those of smaller one. To be precise, the strict monotonicity of topological entropy is demonstrated through the comparison of the maximal and minimal templates as the parameters are varied.

THE ENTROPY OF STATIONARY SOLUTIONS' MAP OF CELLULAR NEURAL NETWORKS

2004 ◽  
Vol 14 (12) ◽  
pp. 4317-4323
Author(s):  
YI WANG ◽  
FANG-YUE CHEN
Keyword(s):  
Neural Networks ◽  
Topological Entropy ◽  
Stationary Solutions ◽  
Cellular Neural Networks ◽  
One Dimensional ◽  
Symbolic Space

In this paper, the entropy of the stationary solutions' map of one-dimensional Cellular Neural Networks with threshold is restudied. Under certain parameters, the map is topological conjugate to a Beruonulli shift of certain symbolic space. Further, the topological entropy of the map can be obtained explicitly as a spacial devil-staircase function.

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.

COMPUTER ASSISTED VERIFICATION OF CHAOS IN THREE-NEURON CELLULAR NEURAL NETWORKS

2007 ◽  
Vol 17 (12) ◽  
pp. 4381-4386 ◽  
Author(s):  
QUAN YUAN ◽  
XIAO-SONG YANG
Keyword(s):  
Neural Networks ◽  
Topological Entropy ◽  
Chaotic Behavior ◽  
Cellular Neural Networks ◽  
Computer Assisted ◽  
Topological Horseshoe ◽  
Poincaré Maps ◽  
New Class ◽  
Numerical Studies ◽  
Connection Matrices

In this paper, we study a new class of simple three-neuron chaotic cellular neural networks with very simple connection matrices. To study the chaotic behavior in these cellular neural networks demonstrated in numerical studies, we resort to Poincaré section and Poincaré map technique and present a rigorous verification of the existence of horseshoe chaos using topological horseshoe theory and the estimate of topological entropy in derived Poincaré maps.

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.

SPATIAL DISORDER OF CELLULAR NEURAL NETWORKS — WITH BIASED TERM

2002 ◽  
Vol 12 (03) ◽  
pp. 525-534 ◽  
Author(s):  
JUNG-CHAO BAN ◽  
SONG-SUN LIN ◽  
CHENG-HSIUNG HSU
Keyword(s):  
Neural Networks ◽  
Stationary Solutions ◽  
Cellular Neural Networks ◽  
One Dimensional ◽  
Spatial Entropy ◽  
Stable Stationary Solutions

This study describes the spatial disorder of one-dimensional Cellular Neural Networks (CNN) with a biased term by applying the iteration map method. Under certain parameters, the map is one-dimensional and the spatial entropy of stable stationary solutions can be obtained explicitly as a staircase function.

PIECEWISE TWO-DIMENSIONAL MAPS AND APPLICATIONS TO CELLULAR NEURAL NETWORKS

2004 ◽  
Vol 14 (07) ◽  
pp. 2223-2228 ◽  
Author(s):  
HSIN-MEI CHANG ◽  
JONG JUANG
Keyword(s):  
Neural Networks ◽  
Cellular Neural Networks ◽  
Two Dimensional ◽  
Smale Horseshoe ◽  
Linear Map ◽  
One Dimensional ◽  
Spatial Chaos

Of concern is a two-dimensional map T of the form T(x,y)=(y,F(y)-bx). Here F is a three-piece linear map. In this paper, we first prove a theorem which states that a semiconjugate condition for T implies the existence of Smale horseshoe. Second, the theorem is applied to show the spatial chaos of one-dimensional Cellular Neural Networks. We improve a result of Hsu [2000].

SPATIAL DISORDER OF CNN — WITH ASYMMETRIC OUTPUT FUNCTION

2001 ◽  
Vol 11 (08) ◽  
pp. 2085-2095 ◽  
Author(s):  
JUNG-CHAO BAN ◽  
KAI-PING CHIEN ◽  
SONG-SUN LIN ◽  
CHENG-HSIUNG HSU
Keyword(s):  
Neural Networks ◽  
Steady State ◽  
Three Dimensional ◽  
Cellular Neural Networks ◽  
Output Function ◽  
One Dimensional ◽  
Spatial Entropy ◽  
The One ◽  
Steady State Solutions

This investigation will describe the spatial disorder of one-dimensional Cellular Neural Networks (CNN). The steady state solutions of the one-dimensional CNN can be replaced as an iteration map which is one dimensional under certain parameters. Then, the maps are chaotic and the spatial entropy of the steady state solutions is a three-dimensional devil-staircase like function.

scholarly journals ESTIMATION OF THE LYAPUNOV SPECTRUM FROM ONE-DIMENSIONAL OBSERVATIONS USING NEURAL NETWORKS

2014 ◽  
pp. 30-34
Author(s):  
Vladimir Golovko
Keyword(s):  
Neural Network ◽  
Dynamical System ◽  
Neural Networks ◽  
Time Series ◽  
Lyapunov Spectrum ◽  
Network Approach ◽  
Neural Network Approach ◽  
One Dimensional ◽  
The Neural Network ◽  
Attractor Dynamics

This paper discusses the neural network approach for computing of Lyapunov spectrum using one dimensional time series from unknown dynamical system. Such an approach is based on the reconstruction of attractor dynamics and applying of multilayer perceptron (MLP) for forecasting the next state of dynamical system from the previous one. It allows for evaluating the Lyapunov spectrum of unknown dynamical system accurately and efficiently only by using one observation. The results of experiments are discussed.

SMALE HORSESHOE OF CELLULAR NEURAL NETWORKS

2000 ◽  
Vol 10 (09) ◽  
pp. 2119-2127 ◽  
Author(s):  
CHENG-HSIUNG HSU
Keyword(s):  
Neural Networks ◽  
Cellular Neural Networks ◽  
Two Dimensional ◽  
Smale Horseshoe ◽  
One Dimensional

The paper shows the spatial disorder of one-dimensional Cellular Neural Networks (CNN) using the iteration map method. Under certain parameters, the map is two-dimensional and the Smale horseshoe is constructed. Moreover, we also illustrate the variant of CNN, closely related to Henón-type and Belykh maps, and discrete Allen–Cahn equations.

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