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https://www.ias.ac.in/article/fulltext/pram/094/0124

Chaotic oscillators; functional connectivity; causality; unidirectional coupling.

In this study, we present a new method for assessing the functional connectivity between the drive and the noisy response chaotic oscillators with significant frequency mismatch. This method is based on the footprint of the drive oscillator on the response oscillator. Specifically, we calculate the magnitude squared coherence between the intrinsic frequency of the drive oscillator and the oscillation frequency of the dynamics of the spectral energy of the response oscillator. The spectral energy of the response oscillator is estimated using a modified S-transform algorithm with a short sliding window. We apply the proposed approach to master–slave Rössler systems and coupled Van der Pol oscillators with a frequency ratio of ~1:4 and show that when the slave signal is contaminated with white Gaussian noise at different signal-to-noise ratios (SNR), the new algorithm is well suited to assess the presence of coupling with $a priori$ known direction in noisy, unidirectionally coupled chaotic oscillators, especially in the case of weak and moderate coupling.

KAZIMIERAS PUKENAS¹

1. Department of Applied Biology and Rehabilitation, Lithuanian Sports University, Sporto 6, 44221 Kaunas, Lithuania

Published

13 August 2020

Manuscript received

9 December 2019

Manuscript revised

17 March 2020

Accepted

13 May 2020

Final version published online

13 August 2020