Inferring causality from highly noisy uni-directionally coupled chaotic oscillators with small frequency mismatch

In the present work, we present a new algorithm for assessing causality in uni-directionally coupled chaotic oscillators with small frequency mismatch 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. To recover the phase at low signal-to-noise ratio, a nonlinear adaptive denoising algorithm based on finding sinusoidal fits to the local neighbourhood of the reconstructed phase space is used. Application of the proposed approach to master-slave Rossler systems showed that the new algorithm is well-suited for assessing the presence and direction of coupling in highly noisy uni-directionally coupled chaotic oscillators, especially in the case of weak and moderate coupling.