We show how to characterize a strange attractor by a set of integers. These are extracted from the chaotic time-series data by first reconstructing the low-period orbits and then determining the template, or knot holder, which supports all periodic orbits embedded in the strange attractor, and the strange attractor itself. The template is identified by a set of integers which therefore characte...

Chaos in nonlinear dynamics occurs widely in physics, chemistry, biology, ecology, secure communications, cryptosystems and many other scientific disciplines. Chaotic systems have many important applications in science and engineering. This paper derives new results for the analysis and adaptive control of a chemical chaotic attractor discovered by Haung (2005). This paper starts with a detaile...

We consider the problem of detection and estimation of chaotic signals in the presence of white Gaussian noise. Traditionally this has been a difficult problem since generalized likelihood ratio tests are difficult to implement due to the chaotic nature of the signals of interest. Based on Poincare's recurrence theorem we derive an algorithm for approximating a chaotic time series with unknown ...

The detection of chaotic behaviors in commodities, stock markets and weather data is usually complicated by large noise perturbation inherent to the underlying system. It is well known, that predictions, from pure deterministic chaotic systems can be accurate mainly in the short term. Thus, it will be important to be able to reconstruct in a robust way the attractor in which evolves the data, i...

In this paper a Lorenz-like system, describing the process of rotating fluid convection, is considered. The present work demonstrates numerically that this system, also like the classical Lorenz system, possesses a homoclinic trajectory and a chaotic self-excited attractor. However, for considered system, unlike the classical Lorenz one, along with self-excited attractor a hidden attractor can ...

We consider blow-out bifurcations of synchronous chaotic attractors on invariant subspaces in coupled chaotic systems with symmetries. Through a blow-out bifurcation, the synchronous chaotic attractor becomes unstable with respect to perturbations transverse to the invariant subspace, and then a new asynchronous chaotic attractor may appear. However, the system symmetry may be preserved or viol...

This paper presents a procedure to transform a chaotic logistic map into a continuous-time delay chaotic system by using sampled-data representation of continuous-time models. Because of this, the chaotic behavior of the resultant scheme is easy to proofread. A numerical illustration is also realized by utilizing Matlab/Simulink, where the new resultant chaotic attractor is shown.

In the present paper we show that inhomogeneity of a continuous self-sustained oscillating medium can be a reason for the onset of chaotic behavior. It has been established that temporal chaotic dynamics typically arises in the medium with a linear mismatch of the natural frequency along a spatial coordinate, whereas a chaotic regime is not characteristic for the medium with randomly distribute...

ABSTRACT: The detection of chaotic behaviors in commodities, stock markets and weather data is usually complicated by large noise perturbation inherent to the underlying system. It is well known, that predictions, from pure deterministic chaotic systems can be accurate mainly in the short term. Thus, it is important to be able to reconstruct in a robust way the attractor in which evolves the da...

In this paper we study chaotic signals generated from Chua’s circuit: in particular we concentrate on the well known spiral attractor. Chaotic signals have a nonstationary nature, and hence the classical Fourier spectrum turns out to be inadequate for the analysis. Instead of it we use TimeFrequency Distributions, a powerful set of tools specifically designed for nonstationary signal analysis. ...