We consider a lattice of coupled logistic maps with periodic boundary condition. We prove that synchronization and almost synchronization occur for the case of 1D lattice with lattice size n = 2, 3, 4 provided the coupling strength c is chosen in a suitable open interval contained in [0, 12 ]. For the case of lattice size n ≥ 4, we also show the numerical results of (almost) synchronized chaoti...

The classical scalar massive field satisfying the Klein-Gordon equation in a finite one-dimensional space interval of periodically varying length with Dirichlet boundary conditions is studied. For the sufficiently small mass, the energy can exponentially grow with time under the same conditions as for the massless case. The proofs are based on estimates of exactly given mass-induced corrections...

x(n + 1) : x(n)exp Jr (n ) (1 x(n) K(n) ] J ' where {r(n)} and {K(n)} are positive w-periodic sequences. Sufficient conditions are obtained for the existence of a positive and globally asymptotically stable w-periodic solution. Counterexamples are given to illustrate that the conclusions in [1] are incorrect. (~) 2003 Elsevier Science Ltd. All rights reserved.

We propose the exact boundary S matrix for breathers of theN = 2 supersymmetric sine-Gordon model. We argue that this S matrix has three independent parameters, in agreement with a recently-proposed action. We also show, contrary to a previous claim, that the “universal” supersymmetric boundary S matrix commutes with two supersymmetry charges. General N = 2 supersymmetric boundary integrable mo...

In the context of coupled periodic waveguides, “couplonics” refers to the rigorous equivalence between continuous wave coupling and localized interactions. We extend it here to a cyclic ternary system, looked upon as the simplest discrete photonic crystal with actual periodic boundary conditions. A linear decomposition on a supermode basis enables one to reduce the original six-wave problem to ...

We deal with the problem of determining an inclusion within an electrical conductor from electrical boundary measurements. Under mild a priori assumptions we establish an optimal stability estimate.

We study the topology of the boundary manifold of a regular neighborhood of a complex projective hypersurface. We show that, under certain Hodge theoretic conditions, the cohomology ring of the complement of the hypersurface functorially determines that of the boundary. When the hypersurface defines a hyperplane arrangement, the cohomology of the boundary is completely determined by the combina...

We prove existence results for travelling waves in discrete, damped, dc-driven sine-Gordon equations with periodic boundary conditions.