Time–frequency representations-based detector of chaos in oscillatory circuits

Rubežić, Vesna; Djurović, Igor; Daković, Miloš

doi:10.1016/j.sigpro.2005.10.006

Cited by 16 publications

(18 citation statements)

References 34 publications

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“…Detection of the chaotic state of signals from circuits was performed in a simpler manner with respect to the existing approaches (Poon and Barahona, 2001; Bandt and Pompe, 2002; Gao, 1999). The obtained detector exhibits better accuracy than the relevant techniques described by Rubežić et al (2006) and Djurović et al (2013) for noisy environments.…”

Section: Introductionmentioning

confidence: 93%

“…However, this problem can be avoided with the proposed algorithm, as the measure is obtained directly from the signal. Additionally, calculating the proposed measure is much simpler than that described in Rubežić et al (2006). Accuracy of the algorithm defined in Rubežić et al (2006) depends on several parameters, the most notably on the applied window width used in the time-frequency representation.…”

Section: The Detector Based On the Average Wavelet Coefficientsmentioning

confidence: 99%

“…Additionally, calculating the proposed measure is much simpler than that described in Rubežić et al (2006). Accuracy of the algorithm defined in Rubežić et al (2006) depends on several parameters, the most notably on the applied window width used in the time-frequency representation. However, the proposed detector depends only on the selection of the mother wavelet and length of the block T .…”

Section: The Detector Based On the Average Wavelet Coefficientsmentioning

confidence: 99%

“…Chaos titration, permutation entropy procedures and recurrence plots have been proposed in Poon and Barahona (2001; Bandt and Pompe, 2002; Gao, 1999). The time-frequency signal analysis detectors of chaotic state are proposed in Rubežić et al (2006; Djurović and Rubežić, 2007; Djurović and Rubežić, 2008). These algorithms properly differentiate chaos and noise for environments of moderate noise levels.…”

Section: Introductionmentioning

confidence: 99%

“…In fact, the WT works as a “mathematical microscope” on a specific part of a signal to extract local structures and singularities (Mallat, 1999; Daubechies, 1992). This makes the WT ideal tool for handling non-stationary and transient signals, as well as for fractal-type structures (Eke et al , 2002), whereas periodic and quasiperiodic trajectories have no significant difference between the windowed (short-time) Fourier (used for chaos detection in Rubežić et al , (2006; Djurović and Rubežić, 2007; Djurović and Rubežić, 2008) and the WT. As the WT is a time-scale representation, it is quite natural to attempt to connect it to the scaling exponent estimation or other tools for scale analysis which are required for the detection of chaos in the oscillating systems.…”

Section: Introductionmentioning

confidence: 99%

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Average wavelet coefficient-based detection of chaos in oscillatory circuits

Rubežić

Djurović

Sejdić

2017

COMPEL

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Purpose The purpose of this paper is to propose a new algorithm for detection of chaos in oscillatory circuits. The algorithm is based on the wavelet transform. Design/methodology/approach The proposed detection is developed by using a specific measure obtained by averaging wavelet coefficients. This measure exhibits various values for chaotic and periodic states. Findings The proposed algorithm is applied to signals from autonomous systems such as the Chua’s oscillatory circuit, the Lorenz chaotic system and non-autonomous systems such as the Duffing oscillator. In addition, the detection is applied to sequences obtained from the logistic map. The results are compared to those obtained with a detrended fluctuation analysis and a time-frequency signal analysis based on detectors of chaotic states. Originality/value In this paper, a new algorithm is proposed for the detection of chaos from a single time series. The proposed technique is robust to the noise influence, having smaller calculation complexity with respect to the state-of-the-art techniques. It is suitable for real-time detection with delay that is about half of the window width.

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