Jonq Juang

Nonsymmetric Algebraic Riccati Equations and Hamiltonian-like Matrices

We consider a nonsymmetric algebraic matrix Riccati equation arising from transport theory. The nonnegative solutions of the equation can be explicitly constructed via the inversion formula of a Cauchy matrix. An error analysis and numerical results are given. We also show a comparison theorem of the nonnegative solutions.

CELLULAR NEURAL NETWORKS: LOCAL PATTERNS FOR GENERAL TEMPLATES

This work investigates the mosaic local patterns for cellular neural networks with general templates. Our results demonstrate that the set of templates can be divided into many nite regions. In each region, the same family of local patterns can be generated. Conversely, our results further demonstrate that some templates can realize a family of local patterns which can be linearly separated by a hyperplane in the conguration space. This study also proposes algorithms for verifying the linear separability for a given family of local patterns and, when it is separable, for obtaining the associated template.

Convergence of an iterative technique for algebraic Matrix Riccati equations and applications to transport theory

Abstract A monotone iterative technique is applied to a class of algebraic matrix Riccati equations that is satisfied by the reflection matrix for linear particle transport in a half-space. The convergence of the iteration as well as the rate of convergence are addressed. Moreover, we show theoretically and numerically that our iterative procedure, in general, is faster than that of Shimizu and Aoki.

Global synchronization in lattices of coupled chaotic systems.

Based on the concept of matrix measures, we study global stability of synchronization in networks. Our results apply to quite general connectivity topology. In addition, a rigorous lower bound on the coupling strength for global synchronization of all oscillators is also obtained. Moreover, by merely checking the structure of the vector field of the single oscillator, we shall be able to determine if the system is globally synchronized.

Synchronous Chaos in Coupled Map Lattices with General Connectivity Topology

The purpose of the paper is to address the synchronous chaos in coupled map lattices with general connectivity topology. Our main results contain the following. First, the master stability functions also hold for general connectivity topology with coupling through a nonlinear function that needs to be exactly the individual chaotic map. Second, the synchronization curve, composed of pieces of transverse Lyapunov exponent curves, is constructed. Third, necessary and sufficient conditions on coupling strength for yielding the synchronous chaos of the system are given. Moreover, the coupling strength

Chaotic difference equations in two variables and their multidimensional perturbations

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Nonlinear dynamics of self-pulsating laser diodes under external drive.

giving the fastest convergence rate of the initial values toward the synchronous state is explicitly obtained. It is also proved that such

Subcarrier multiplexing by chaotic multitone modulation

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Perturbed block circulant matrices and their application to the wavelet method of chaotic control

is independent of the choice of the individual map. Finally, our results here can be applied to address questions of wavelength bifurcations and size instability.

THE SPATIAL ENTROPY OF TWO-DIMENSIONAL SUBSHIFTS OF FINITE TYPE

We consider difference equations � λ(yn ,y n+1 ,...,y n+m) = 0, n ∈ Z ,o f order m with parameter λ close to that exceptional value λ0 for which the functiondepends on two variables: � λ0 (x0 ,...,x m) = ξ(xN ,x N +L) with 0 N, N + L m. It is also assumed that for the equation ξ(x, y) = 0, there is a branch y = ϕ(x) with positive topological entropy htop(ϕ). Under these assumptions we prove that in the set of bi-infinite solutions of the difference equation with λ in some neighbourhood of λ0, there is a closed (in the product topology) invariant set to which the restriction of the shift map has topological entropy arbitrarily close to htop(ϕ)/|L|, and moreover, orbits of this invariant set depend continuously on λ not only in the product topology but also in the uniform topology. We then apply this result to establish chaotic behaviour for Arneodo-Coullet-Tresser maps near degenerate ones, for quadratic volume preserving automorphisms of R 3 and for several lattice models including the generalized cellular neural networks (CNNs), the time discrete version of the CNNs and coupled Chuas circuit.