Journal of Applied Nonlinear Dynamics 12(1) (2023) 31--37 | DOI:10.5890/JAND.2023.03.002

Kazimieras Pukenas

Department of Health Promotion and Rehabilitation, Lithuanian Sports University, Sporto 6, LT-44221, Kaunas, Lithuania

Abstract

In this study, we present a new method for assessing the directional coupling between drive and noisy response chaotic oscillators with significant frequency mismatch. This method is based on the phase-amplitude coupling between the drive oscillator and response oscillator. Specifically, the weak phase-amplitude coupling effect is calculated as the magnitude squared coherence between the intrinsic frequency of the drive oscillator and the oscillation frequency of the dynamics of the bispectral energy of the response oscillator. The bispectral energy of the response oscillator at the selected combination of the frequencies is estimated using the Blackman-Harris sliding window with a sharp peak at the central frequency, and the magnitude squared coherence is calculated based on the moving block-bootstrap (MBB) technique. Application of the proposed approach to master-slave R\"{o}ssler systems and coupled Van der Pol oscillators with a frequency ratio of $ {\sim}$1:4 show that the new algorithm is well-suited for assessing the presence of coupling with a priori known direction between master and noisy slave oscillators at signal-to-noise ratios (SNR) up to 12 dB, especially in the case of weak and moderate coupling.

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