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Discontinuity, Nonlinearity, and Complexity 12(4) (2023) 715--722 | DOI:10.5890/DNC.2023.12.001

Kazimieras Pukenas

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

Lithuania

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Abstract

In the present work, we present a new algorithm for assessing causality in uni-directionally weakly coupled chaotic oscillators embedded in heavy white Gaussian noise. This method is based on the correlation between changes in the phase dynamics of the slave oscillator and the dynamics of the phase difference between the oscillators. This can be applied when the phase difference is determined by the intrinsic frequencies of the oscillators, and the effect of the phase slip of the slave oscillator on the phase difference is nonsignificant. To recover the phase at a low signal-to-noise ratio (SNR), the wrapped phase is converted into sine and cosine formats and then denoised using a Fourier transformation followed by a recalculation of the wrapped phase values through those filtered terms. Application of the proposed approach to master-slave R\"{o}ssler systems and coupled Stuart--Landau oscillators showed that the new algorithm is well-suited for assessing the presence and direction of coupling in highly noisy chaotic oscillators weakly coupled in a uni-directional manner. Specifically, directional coupling was reliably detected at a SNR of up to 0 dB for chaotic R\"{o}ssler systems and for Stuart--Landau oscillators.

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