Article

Modified correlation entropy estimation for a noisy chaotic time series.

International Centre for Water Hazard and Risk Management, Public Works Research Institute, 305-8516 Tsukuba, Japan.
Chaos (Woodbury, N.Y.) (Impact Factor: 1.8). 06/2010; 20(2):023104. DOI: 10.1063/1.3382013
Source: PubMed

ABSTRACT A method of estimating the Kolmogorov-Sinai (KS) entropy, herein referred to as the modified correlation entropy, is presented. The method can be applied to both noise-free and noisy chaotic time series. It has been applied to some clean and noisy data sets and the numerical results show that the modified correlation entropy is closer to the KS entropy of the nonlinear system calculated by the Lyapunov spectrum than the general correlation entropy. Moreover, the modified correlation entropy is more robust to noise than the correlation entropy.

0 Bookmarks
 · 
231 Views
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: This project studies the dynamics of electromechanical systems, a Faraday disk coupled with a Bullard Dynamo. First the individual systems are stud-ied in detail. This is followed by the study of the coupled system. We find the fixed points, dynamical regimes for different set of parameters, and characterize the dynamics, by various measures of irregularity.
    07/2013, Degree: Summer Fellowship
  • [Show abstract] [Hide abstract]
    ABSTRACT: Time series is widely exploited to study the innate character of the complex chaotic system. Existing chaotic models are weak in modeling accuracy because of adopting either error minimization strategy or an acceptable error to end the modeling process. Instead, interpolation can be very useful for solving differential equations with a small modeling error, but it is also very difficult to deal with arbitrary-dimensional series. In this paper, geometric theory is considered to reduce the modeling error, and a high-precision framework called Series-NonUniform Rational B-Spline (S-NURBS) model is developed to deal with arbitrary-dimensional series. The capability of the interpolation framework is proved in the validation part. Besides, we verify its reliability by interpolating Musa dataset. The main improvement of the proposed framework is that we are able to reduce the interpolation error by properly adjusting weights series step by step if more information is given. Meanwhile, these experiments also demonstrate that studying the physical system from a geometric perspective is feasible.
    Chaos (Woodbury, N.Y.) 09/2013; 23(3):033132. · 1.80 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: The time evolution of the output of a semiconductor laser subject to delayed optical feedback can exhibit high-dimensional chaotic fluctuations. In this contribution, our aim is to quantify the degree of unpredictability of this hyperchaotic time evolution. To that end, we estimate permutation entropy, a novel information-theory-derived quantifier particularly robust in a noisy environment. The permutation entropy is defined as a functional of a symbolic probability distribution, evaluated using the Bandt-Pompe recipe to assign a probability distribution function to the time series generated by the chaotic system. This measure quantifies the diversity of orderings present in the associated time series. In order to evaluate the performance of this novel quantifier, we compare with the results obtained by using a more standard chaos quantifier, namely the Kolmogorov-Sinai entropy. Here, we present numerical results showing that the permutation entropy, evaluated at specific time-scales involved in the chaotic regime of the semiconductor laser subject to optical feedback, give valuable information about the degree of unpredictability of the chaotic laser dynamics. The influence of additive observational noise on the proposed tool is also investigated.
    IEEE Journal of Selected Topics in Quantum Electronics 01/2011; 17(5):1250-1257. · 4.08 Impact Factor

Full-text (2 Sources)

Download
34 Downloads
Available from
Jun 5, 2014