SPATIAL DISORDER OF CNN — WITH ASYMMETRIC OUTPUT FUNCTION

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.

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SPATIAL DISORDER OF CELLULAR NEURAL NETWORKS — WITH BIASED TERM

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127402004541 ◽

2002 ◽

Vol 12 (03) ◽

pp. 525-534 ◽

Cited By ~ 10

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.

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EXACT NUMBER OF MOSAIC PATTERNS IN CELLULAR NEURAL NETWORKS

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127401002900 ◽

2001 ◽

Vol 11 (06) ◽

pp. 1645-1653 ◽

Cited By ~ 9

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.

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Traveling Waves for Delayed Cellular Neural Networks with Nonmonotonic Output Functions

Abstract and Applied Analysis ◽

10.1155/2014/490161 ◽

2014 ◽

Vol 2014 ◽

pp. 1-11 ◽

Cited By ~ 2

Author(s):

Zhi-Xian Yu ◽

Rong Yuan ◽

Cheng-Hsiung Hsu ◽

Ming-Shu Peng

Keyword(s):

Neural Networks ◽

Traveling Waves ◽

Signal Transmission ◽

Distributed Delay ◽

Traveling Wave Solutions ◽

Cellular Neural Networks ◽

Switching Speed ◽

One Dimensional ◽

The One ◽

Nondecreasing Functions

This work investigates traveling waves for a class of delayed cellular neural networks with nonmonotonic output functions on the one-dimensional integer latticeZ. The dynamics of each given cell depends on itself and its nearestmleft orlright neighborhood cells with distributed delay due to, for example, finite switching speed and finite velocity of signal transmission. Our technique is to construct two appropriate nondecreasing functions to squeeze the nonmonotonic output functions. Then we construct a suitable wave profiles set and derive the existence of traveling wave solutions by using Schauder's fixed point theorem.

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THREE-DIMENSIONAL CELLULAR NEURAL NETWORKS AND PATTERN GENERATION PROBLEMS

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127408020781 ◽

2008 ◽

Vol 18 (04) ◽

pp. 957-984 ◽

Cited By ~ 5

Author(s):

JUNG-CHAO BAN ◽

SONG-SUN LIN ◽

YIN-HENG LIN

Keyword(s):

Neural Networks ◽

Transition Matrix ◽

Finite Lattice ◽

Three Dimensional ◽

Recursive Formula ◽

Cellular Neural Networks ◽

Pattern Generation ◽

Transition Matrices ◽

Spatial Entropy ◽

Local Patterns

This work investigates three-dimensional pattern generation problems and their applications to three-dimensional Cellular Neural Networks (3DCNN). An ordering matrix for the set of all local patterns is established to derive a recursive formula for the ordering matrix of a larger finite lattice. For a given admissible set of local patterns, the transition matrix is defined and the recursive formula of high order transition matrix is presented. Then, the spatial entropy is obtained by computing the maximum eigenvalues of a sequence of transition matrices. The connecting operators are used to verify the positivity of the spatial entropy, which is important in determining the complexity of the set of admissible global patterns. The results are useful in studying a set of global stationary solutions in various Lattice Dynamical Systems and Cellular Neural Networks.

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Research on the Issue of LED’s Cooling Based on Heat Conduction Equations

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.507.137 ◽

2012 ◽

Vol 507 ◽

pp. 137-141

Author(s):

Zhi Qin Huang ◽

Pei Ying Quan ◽

Yong Qing Pan

Keyword(s):

Heat Conduction ◽

Steady State ◽

Heat Conduction Equation ◽

Rapid Development ◽

Three Dimensional ◽

Conduction Equation ◽

Dimensional Model ◽

Three Dimensional Model ◽

One Dimensional ◽

The One

With the rapid development of power type LED, the issue of the cooling of LED has been prominent. How to make the heat generated by LED chip go out quickly in order to cool the LED chip has become an urgent problem. The form of heat goes through the substrate has been widely used and has become the best way to solve the heat problem. There are three types of LED substrate. They are metal substrate, ceramic substrate and composite substrate. At first, In this paper I analyze the theoretical of three-dimensional non-steady state and steady state heat conduction equation, then the three-dimensional model is simplified as one-dimensional model and I get the results of heat conduction equation under the one-dimensional stationary and non-steady state.

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CELLULAR NEURAL NETWORKS: MOSAIC PATTERNS, BIFURCATION AND COMPLEXITY

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127406014575 ◽

2006 ◽

Vol 16 (01) ◽

pp. 47-57 ◽

Cited By ~ 1

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.

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MULTIPLE BIFURCATION ANALYSIS AND SPATIOTEMPORAL PATTERNS IN A 1-D GIERER–MEINHARDT MODEL OF MORPHOGENESIS

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127410026289 ◽

2010 ◽

Vol 20 (04) ◽

pp. 1007-1025 ◽

Cited By ~ 19

Author(s):

JIANXIN LIU ◽

FENGQI YI ◽

JUNJIE WEI

Keyword(s):

Steady State ◽

Bifurcation Analysis ◽

Reaction Diffusion ◽

Spatiotemporal Patterns ◽

Fixed Boundary ◽

One Dimensional ◽

Steady State Bifurcation ◽

The One ◽

Steady State Solutions ◽

Fixed Boundary Condition

A reaction–diffusion Gierer–Meinhardt model of morphogenesis subject to Dirichlet fixed boundary condition in the one-dimensional spatial domain is considered. We perform a detailed Hopf bifurcation analysis and steady state bifurcation analysis to the system. Our results suggest the existence of spatially nonhomogenous periodic orbits and nonconstant positive steady state solutions, which imply the possibility of complex spatiotemporal patterns of the system. Numerical simulations are carried out to support our theoretical analysis.

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Exploring the Multidimensional Facets of Authoritarianism: Authoritarian Aggression and Social Dominance Orientation

Swiss Journal of Psychology ◽

10.1024/1421-0185.67.1.51 ◽

2008 ◽

Vol 67 (1) ◽

pp. 51-60 ◽

Cited By ~ 26

Author(s):

Stefano Passini

Keyword(s):

Social Dominance ◽

Factor Model ◽

Three Dimensional ◽

Social Dominance Orientation ◽

Model Fit ◽

Regression Analyses ◽

One Dimensional ◽

Confirmatory Factor ◽

The One ◽

Better Than

The relation between authoritarianism and social dominance orientation was analyzed, with authoritarianism measured using a three-dimensional scale. The implicit multidimensional structure (authoritarian submission, conventionalism, authoritarian aggression) of Altemeyer’s (1981, 1988) conceptualization of authoritarianism is inconsistent with its one-dimensional methodological operationalization. The dimensionality of authoritarianism was investigated using confirmatory factor analysis in a sample of 713 university students. As hypothesized, the three-factor model fit the data significantly better than the one-factor model. Regression analyses revealed that only authoritarian aggression was related to social dominance orientation. That is, only intolerance of deviance was related to high social dominance, whereas submissiveness was not.

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