The discrete distribution of homoclinic orbits has been investigated numerically and experimentally in a CO2 laser with feedback. The narrow chaotic ranges appear consequently when a laser parameter (bias voltage or feedback gain) changes exponentially. Up to six consecutive chaotic windows have been observed in the numerical simulation as well as in the experiments. Every subsequent increase i...

In this work, a new scheme of image encryption based on chaos and Fast Walsh Transform (FWT) has been proposed. We used two chaotic logistic maps and combined chaotic encryption methods to the two-dimensional FWT of images. The encryption process involves two steps: firstly, chaotic sequences generated by the chaotic logistic maps are used to permute and mask the intermediate results or array o...

The purpose of this letter is to define a distance on the underlying phase space of a chaotic map, based on natural invariant density of the map. It is observed that for logistic map this distance is equivalent to Wootters’ statistical distance. This distance becomes the Euclidean distance for a map with constant invariant density. ∗Postal Address: 1110, 36-C, Chandigarh -160014, India

We describe up to conjugacy all unimodal and bimodal maps that are chaotic, by giving necessary and sufficient conditions for unimodal and bimodal maps of slopes ±s to be transitive.

In the family of area-contracting Hénon-like maps with zero topological entropy we show that there are maps with infinitely many moduli of stability. Thus one cannot find all the possible topological types for non-chaotic area-contracting Hénon-like maps in a family with finitely many parameters. A similar result, but for the chaotic maps in the family, became part of the folklore a short time ...

Multistability is characterized by the occurrence of multiple coexisting attractors. We introduce a family of maps that possess this property and in particular exhibits coexisting chaotic attractors. In this family not only the maps’ parameters can be varied but also their dimension. So, four types of multistable attractors, equilibria, periodic orbits, quasi-periodic orbits and chaotic attract...

The quantum evolution maps of closed chaotic quantum graphs are unitary and known to have universal spectral correlations matching predictions of random matrix theory. In chaotic graphs with absorption the quantum maps become nonunitary. We show that their spectral statistics exhibit universality at the soft edges of the spectrum. The same spectral behavior is observed in many classical nonunit...

Title of dissertation: SYNCHRONIZATION IN CHAOTIC SYSTEMS: COUPLING OF CHAOTIC MAPS, DATA ASSIMILATION, AND WEATHER FORECASTING Seung-Jong Baek, Doctor of Philosophy, 2007 Dissertation directed by: Distinguished University Professor Edward Ott Department of Electrical and Computer Engineering The theme of this thesis is the synchronization of coupled chaotic systems. Background and introductory...

Rényi entropy and generalized complexity measures are used to describe the chaotic behaviour of dynamical systems. These measures are found to be sensitive to the fine details of the Rössler and the Duffing maps. They are good descriptors of chaotic behaviour. Periodic windows and the fractal character of the chaotic dynamics are nicely detected.

Abstract : A route to chaos is studied in 3-dimensional maps of logistic type. Mechanisms of period doubling for invariant closed curves (ICC) are found for specific 3-dimensional maps. These bifurcations cannot be observed for ICC in the 2-dimensional case. When the parameter of the system is modified, localized oscillations occur on the ICC that give rise to weakly chaotic rings, then to chao...