We study the synchronization properties of a lattice of chaotic piecewise linear maps. The coupling strength decreases with the lattice distance in a power-law fashion. We obtain the Lyapunov spectrum of the coupled map lattice and investigate the relation between spatiotemporal chaos and synchronization of amplitudes and phases, using suitable numerical diagnostics.

In this text we are interested in spectral properties of discrete Laplace operators deened on lattices based on nitely-ramiied self-similar sets. The basic example is the lattice based on the Sierpinski gasket. We introduce a new renormalization map which appears to be a rational self-map of a compact complex manifolds. We relate some characteristics of its dynamics with some characteristics of...

The Self-Organizing Map (SOM) can be used for forming overviews of multivariate data sets and for visualizing them on graphical map displays. Each map location represents certain kinds of data items and the value of a variable in the representations can be visualized in the corresponding locations on the map display. Such component plane displays contain all the information needed for interpret...

The analytical structure of some generalizations of the circle map is given. Also a generalization of off centre reflection is studied. The stability of Ito-Glass coupled map lattice is studied.

C is self-dual if C = C⊥. We define a Type II code over R as a self-dual code with Eudidean weights divisible by 4k. We consider the natural projection ρ from Z to R, then this map induces the map (also we denote ρ ) from Zn to Rn. We set Λ(C) = 1 √ 2k ρ−1(C). Theorem 1 If C is self-duel code of length n over R, then the lattice Λ(C) is an n-dimensioal unimodular lattice. Moreover if C is Type ...

We revisit the globally coupled map lattice (GCML) and also propose a new extended globally coupled map lattice (EGCML) with an inverse power law interaction. In GCML we clarify the mechanism of the basic posi-nega switch in the two-cluster regime. We show that there is a natural mechanism in GCML which guarantees no mixing of maps across their mean field in the chaotic transient process. In th...

A wide range of coupled map lattices is shown to have identical pattern sequences. It is found that the wave type solutions in their respective pattern selection regimes scale linearly with the coupling range indicating the existence of a continuum limit. The findings are used to introduce a very simple novel type of spatially extended map which can serve as a representative for this class of c...