Average wavelet coefficient-based detection of chaos in oscillatory circuits

• Vesna Rubežić ^[1] ; Igor Djurović ^[1] ; Ervin Sejdić ^[2]
  1. [1] University of Montenegro

     University of Montenegro

     Montenegro

     
  2. [2] University of Pittsburgh

     University of Pittsburgh

     City of Pittsburgh, Estados Unidos

     
• Localización: Compel: International journal for computation and mathematics in electrical and electronic engineering, ISSN 0332-1649, Vol. 36, Nº 1, 2017, págs. 188-201
• Idioma: inglés
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• Resumen

  • 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.