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 $$\sim $$ ∼ 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.

中文翻译：

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一种有效的算法，用于推断驱动器和具有显着频率失配的噪声响应混沌振荡器之间的功能连接

在这项研究中，我们提出了一种评估驱动器和具有显着频率失配的噪声响应混沌振荡器之间的功能连接的新方法。该方法基于驱动振荡器在响应振荡器上的占位面积。具体来说，我们计算驱动振荡器的固有频率与响应振荡器的谱能量动力学的振荡频率之间的幅度平方相干性。使用带有短滑动窗口的改进 S 变换算法来估计响应振荡器的频谱能量。我们将所提出的方法应用于主从 Rössler 系统和耦合 Van der Pol 振荡器，频率比为 $$\sim $$ ∼ 1：