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.

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.

CHAOTIC STATIONARY SOLUTIONS OF CELLULAR NEURAL NETWORKS

2003 ◽  
Vol 13 (11) ◽  
pp. 3499-3504 ◽  
Author(s):  
FANG-YUE CHEN ◽  
ZENG-RONG LIU
Keyword(s):  
Neural Networks ◽  
Stationary Solution ◽  
Main Tool ◽  
Stationary Solutions ◽  
Cellular Neural Networks ◽  
Cantor Set ◽  
Two Dimensional ◽  
One Dimensional ◽  
Specific Term

This study describes the chaotic stationary solutions of one-dimensional Cellular Neural Networks (CNN) without inputs with a specific term by applying the iteration map method. Under perfectly determined specific parameters, the map which corresponds to the stationary solution of CNN is two-dimensional and has a hyperbolic invariant Cantor set on which it is topologically conjugate to a two-sided shift of symbols space. The used main tool is the Conley–Moser conditions.

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.

CELLULAR NEURAL NETWORKS: ASYMMETRIC SPACE-DEPENDENT TEMPLATES, MOSAIC PATTERNS, AND SPATIAL CHAOS

2004 ◽  
Vol 14 (08) ◽  
pp. 2655-2665 ◽  
Author(s):  
LARRY TURYN
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Hexagonal Lattice ◽  
Cellular Neural Network ◽  
Cellular Neural Networks ◽  
Integer Lattice ◽  
Spatial Entropy ◽  
Spatial Chaos

We consider a Cellular Neural Network (CNN), with a bias term, on the integer lattice ℤ2in the plane ℝ2. Space-dependent, asymmetric couplings (templates) appropriate for CNN in the hexagonal lattice on ℝ2are studied. We characterize the mosaic patterns and study their spatial entropy. It appears that for this problem, asymmetry of the template has a more robust effect on the spatial entropy than does the sign of a parameter in the templates.

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.

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.

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].

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.

CELLULAR NEURAL NETWORKS: SPACE-DEPENDENT TEMPLATE, MOSAIC PATTERNS AND SPATIAL CHAOS

2002 ◽  
Vol 12 (08) ◽  
pp. 1717-1730 ◽  
Author(s):  
JONQ JUANG ◽  
SHIH-FENG SHIEH ◽  
LARRY TURYN
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Hexagonal Lattice ◽  
Cellular Neural Network ◽  
Cellular Neural Networks ◽  
Invariant Set ◽  
Integer Lattice ◽  
Translation Invariant ◽  
Spatial Entropy ◽  
Spatial Chaos

We consider a Cellular Neural Network (CNN) with a bias term in the integer lattice tenpoint ℤ2 on the plane tenpoint ℤ2. We impose a space-dependent coupling (template) appropriate for CNN in the hexagonal lattice on tenpoint ℤ2. Stable mosaic patterns of such CNN are completely characterized. The spatial entropy of a tenpoint (p1, p2)-translation invariant set is proved to be well-defined and exists. Using such a theorem, we are also able to address the complexities of resulting mosaic patterns.

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