Browsing by Author "Ban, JC"

Now showing 1 - 5 of 5

Devil's staircase of gap maps
(2003-01-01)
Ban, JC
;
Hsu, CH
;
Lin, SS
;
應用數學系
;
Department of Applied Mathematics
This study demonstrates the devil's staircase structure of topological entropy functions for one-dimensional symmetric unimodal maps with a gap inside. The results are obtained by using kneading theory and are helpful in investigating the communication of chaos.
Exact number of mosaic patterns in cellular neural networks
(2001-06-01)
Ban, JC
;
Lin, SS
;
Shih, CW
;
應用數學系
;
Department of Applied Mathematics
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 x 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.
Patterns generation and transition matrices in multi-dimensional lattice models
(2005-08-01)
Ban, JC
;
Lin, SS
;
應用數學系
;
Department of Applied Mathematics
In this paper we develop a general approach for investigating pattern generation problems in multi-dimensional lattice models. Let S be a set of p symbols or colors, Z(N) a fixed finite rectangular sublattice of Z(d), d >= 1 and N a d-tuple of positive integers. Functions U : Z(d) --> S and U-N : Z(N) --> S are called a global pattern and a local pattern on ZN, respectively. We introduce an ordering matrix X-N for Sigma(N), the set of all local patterns on Z(N). For a larger finite lattice Z((N) over tilde) (N) over tilde >= N, we derive a recursion formula to obtain the ordering matrix X-(N) over tilde of Sigma((N) over tilde) from XN. For a given basic admissible local patterns set 13 C Ely, the transition matrix T-N(B) is defined. For each (N) over tilde >= N denoted by Sigma((N) over tilde)(B) the set of all local patterns which can be generated from B, the cardinal number of Sigma((N) over tilde)(B) is the sum of entries of the transition matrix T-(N) over tilde(B) which can be obtained from T-N(B) recursively. The spatial entropy h(B) can be obtained by computing the maximum eigenvalues of a sequence of transition matrices T-n(B). The results can be applied to study the set of global stationary solutions in various Lattice Dynamical Systems and Cellular Neural Networks.
Spatial disorder of cellular neural networks with biased term
(2002-03-01)
Ban, JC
;
Lin, SS
;
Hsu, CH
;
應用數學系
;
Department of Applied Mathematics
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
(2001-08-01)
Ban, JC
;
Chien, KP
;
Lin, SS
;
Hsu, CH
;
應用數學系
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.