Average wavelet coefficient-based detection of chaos in oscillatory circuits

Abstract

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.

Citation

Rubežić, V., Djurović, I. and Sejdić, E. (2017), "Average wavelet coefficient-based detection of chaos in oscillatory circuits", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 36 No. 1, pp. 188-201. https://doi.org/10.1108/COMPEL-05-2016-0198