The collective behavior of locally coupled-map lattices is investigated when the connections are defined on fractal geometries, such as generalized Sierpinski gaskets embedded in d-dimensional Euclidean spaces. The collective states are described through the mean fields of the networks. Periodic...

This article investigates the H∞ synchronization problem for a general class of chaotic systems. Based on Lyapunov theory, linear matrix inequality (LMI) and linear matrix equality (LME) formulation, the output feedback controller is established to not only guarantee stable synchronization of...

A nonextensive thermostatic approach to chaotic dynamical systems is developed by expressing generalized Tsallis distribution as escort distribution. We explicitly consider the thermodynamic limit and also derive the Legendre Transform structure. As an application, bit variance is calculated for...

The coexistence of ordered and chaotic dynamics in one and the same system has been detected already several years ago. A thorough description of a complex dynamical system, both from a mechanical and from a statistical point of view, requires the determination of the level of order and...

We propose an information-theoretic framework for analyzing control systems based on the close relationship of controllers to communication channels. A communication channel takes an input state and transforms it into an output state. A controller, similarly, takes the initial state of a system...

In this work, we investigate the relations among the Unstable Dimension Variability (UDV) and phase space dimensions in a coupled map lattice with diffusive coupling. Studying a simple system with UDV at low dimensions, we give theoretical support and numerical evidence to the statement that,...

In this article we present a methodology under which stability and synchronization of a dynamical master/slave system configuration are preserved under modification through matrix multiplication. The objective is to show that under a defined multiplicative group, hyperbolic critical points are...

We study phase synchronization between atmospheric variables such as daily mean temperature and daily precipitation records. We find significant phase synchronization between records of Oxford and Vienna as well as between the records of precipitation and temperature in each city. To find the...

The chaotic dynamics of a random walker in a quenched environment is studied via the thermodynamic formalism of Ruelle, Sinai, and Bowen, in which chaotic properties are expressed in terms of a free energy-type function, ψ(β), of an inverse temperature-like parameter, β. Localization...