CELLULAR NEURAL NETWORKS: MOSAIC PATTERNS, BIFURCATION AND COMPLEXITY

2006 ◽  
Vol 16 (01) ◽  
pp. 47-57 ◽  
Author(s):  
JONQ JUANG ◽  
CHIN-LUNG LI ◽  
MING-HUANG LIU
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Source Term ◽  
Cellular Neural Network ◽  
Cellular Neural Networks ◽  
Output Function ◽  
Transition Matrices ◽  
One Dimensional ◽  
Bifurcation Phenomenon

We study a one-dimensional Cellular Neural Network with an output function which is nonflat at infinity. Spatial chaotic regions are completely characterized. Moreover, each of their exact corresponding entropy is obtained via the method of transition matrices. We also study the bifurcation phenomenon of mosaic patterns with bifurcation parameters z and β. Here z is a source (or bias) term and β is the interaction weight between the neighboring cells. In particular, we find that by injecting the source term, i.e. z ≠ 0, a lot of new chaotic patterns emerge with a smaller interaction weight β. However, as β increases to a certain range, most of previously observed chaotic patterns disappear, while other new chaotic patterns emerge.

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.

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.

Study of Highway Crack Diagnosis Based on Cellular Neural Network

2013 ◽  
Vol 427-429 ◽  
pp. 2013-2017
Author(s):  
Sheng Zhuo Yao ◽  
Guo Dong Li ◽  
Fu Xin Zhang ◽  
Lin Ge
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Image Processing ◽  
Cellular Neural Network ◽  
Cellular Neural Networks ◽  
Quality Information ◽  
Image Detection ◽  
The Road ◽  
Standard Level ◽  
On The Road

Road quality information detect system is an important component in architecture quality detect system, also is the basement of successfully working of other related project for the whole country. The study of detecting the road crack is the key to insure the security of accurately detect the road quality in transportation system. In this paper, we come up with a fixed way of road undersized rift image detection by using cellular neural networks. By image processing, building rift networks and details networks and adding the model of similarity undersized rift networks. It can avoid the problem that can not accurately detect undersized crack by only taking the crack feature value. The experiment proved that fixed crack detect computing is easy to do, more accurate to detect the undersized cracks on the road and can reach the standard level of current detect technique.

scholarly journals REALIZATION AND BIFURCATION OF BOOLEAN FUNCTIONS VIA CELLULAR NEURAL NETWORKS

2005 ◽  
Vol 15 (07) ◽  
pp. 2109-2129 ◽  
Author(s):  
FANGYUE CHEN ◽  
GUANRONG CHEN
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Boolean Function ◽  
Boolean Functions ◽  
Cellular Neural Network ◽  
Cellular Neural Networks ◽  
Gene Bank ◽  
Engineering Applications ◽  
Binary Input

In this work, we study the realization and bifurcation of Boolean functions of four variables via a Cellular Neural Network (CNN). We characterize the basic relations between the genes and the offsets of an uncoupled CNN as well as the basis of the binary input vectors set. Based on the analysis, we have rigorously proved that there are exactly 1882 linearly separable Boolean functions of four variables, and found an effective method for realizing all linearly separable Boolean functions via an uncoupled CNN. Consequently, any kind of linearly separable Boolean function can be implemented by an uncoupled CNN, and all CNN genes that are associated with these Boolean functions, called the CNN gene bank of four variables, can be easily determined. Through this work, we will show that the standard CNN invented by Chua and Yang in 1988 indeed is very essential not only in terms of engineering applications but also in the sense of fundamental mathematics.

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.

EXACT NUMBER OF MOSAIC PATTERNS IN CELLULAR NEURAL NETWORKS

2001 ◽  
Vol 11 (06) ◽  
pp. 1645-1653 ◽  
Author(s):  
JUNG-CHAO BAN ◽  
SONG-SUN LIN ◽  
CHIH-WEN SHIH
Keyword(s):  
Neural Networks ◽  
Boundary Conditions ◽  
Cellular Neural Networks ◽  
Transition Matrices ◽  
Lattice Systems ◽  
Range Interaction ◽  
One Dimensional ◽  
Various Boundary Conditions ◽  
Exact Number ◽  
The One

This work investigates mosaic patterns for the one-dimensional cellular neural networks with various boundary conditions. These patterns can be formed by combining the basic patterns. The parameter space is partitioned so that the existence of basic patterns can be determined for each parameter region. The mosaic patterns can then be completely characterized through formulating suitable transition matrices and boundary-pattern matrices. These matrices generate the patterns for the interior cells from the basic patterns and indicate the feasible patterns for the boundary cells. As an illustration, we elaborate on the cellular neural networks with a general 1 × 3 template. The exact number of mosaic patterns will be computed for the system with the Dirichlet, Neumann and periodic boundary conditions respectively. The idea in this study can be extended to other one-dimensional lattice systems with finite-range interaction.

scholarly journals Dynamic properties of cellular neural networks

1993 ◽  
Vol 6 (2) ◽  
pp. 107-116 ◽  
Author(s):  
Angela Slavova
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Dynamic Properties ◽  
Cellular Neural Network ◽  
State Equation ◽  
Cellular Neural Networks ◽  
New Approach ◽  
New Class ◽  
Continuous State Space ◽  
Continuous State

Dynamic behavior of a new class of information-processing systems called Cellular Neural Networks is investigated. In this paper we introduce a small parameter in the state equation of a cellular neural network and we seek for periodic phenomena. New approach is used for proving stability of a cellular neural network by constructing Lyapunov's majorizing equations. This algorithm is helpful for finding a map from initial continuous state space of a cellular neural network into discrete output. A comparison between cellular neural networks and cellular automata is made.

CELLULAR NEURAL NETWORKS FOR EDGE DETECTION

2007 ◽  
Vol 17 (04) ◽  
pp. 1323-1328
Author(s):  
GIUSEPPE GRASSI ◽  
PIETRO VECCHIO ◽  
EUGENIO DI SCIASCIO ◽  
LUIGI A. GRIECO
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Edge Detection ◽  
Cellular Neural Network ◽  
Cellular Neural Networks ◽  
Detection Technique ◽  
Hardware Implementations ◽  
Rigorous Model ◽  
Better Than

This Letter presents an effective edge detection technique based on the cellular neural network paradigm. The approach exploits a rigorous model of the image contours and takes into account some electrical restrictions of existing hardware implementations. The method yields accurate results, better than the ones achievable by other cellular neural network-based techniques.

HYPERCHAOS IN RTD-BASED CELLULAR NEURAL NETWORKS

2008 ◽  
Vol 18 (11) ◽  
pp. 3439-3446 ◽  
Author(s):  
FENG-JUAN CHEN ◽  
JI-BIN LI
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Lyapunov Exponents ◽  
Cellular Neural Network ◽  
Cellular Neural Networks ◽  
Phase Portraits

In this paper, a hyperchaotic RTD-based cellular neural network is proposed and its hyperchaotic dynamics is demonstrated. The Lyapunov exponents spectrum is presented, and some typical Lyapunov exponents are calculated in a range of parameters. Several important phase portraits are presented as well.

STAR CELLULAR NEURAL NETWORKS FOR ASSOCIATIVE AND DYNAMIC MEMORIES

2004 ◽  
Vol 14 (05) ◽  
pp. 1725-1772 ◽  
Author(s):  
MAKOTO ITOH ◽  
LEON O. CHUA
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Cellular Neural Network ◽  
Cellular Neural Networks ◽  
Phase Relations ◽  
Associative Memories ◽  
Central System ◽  
Local Oscillators ◽  
System A ◽  
Output Pattern

In this paper, we propose a Star cellular neural network (Star CNN) for associative and dynamic memories. A Star CNN consists of local oscillators and a central system. All oscillators are connected to a central system in the shape of a Star, and communicate with each other through a central system. A Star CNN can store and retrieve given patterns in the form of synchronized chaotic states with appropriate phase relations between the oscillators (associative memories). Furthermore, the output pattern can occasionally travel around the stored patterns, their reverse patterns, and new relevant patterns which are called spurious patterns (dynamic memories).

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