Detecting coherence between oscillators in heavy-noise environments with a moving block bootstrap

In this paper, a novel algorithm based on the moving block-bootstrap (MBB) technique for the detection of coherence between oscillators in heavy-noise environments is proposed. To verify the null hypothesis of absent significant coherence against the alternative, the average coherence of MBB resampled data is compared with a certain threshold over all frequencies. The threshold is defined as the upper bound of a 95 % confidence interval for bootstrapping coherence performed with independent resampling indexes for both time series, so the dependence between the time series under consideration is destroyed. The benefits of the proposed method are illustrated by simulations of the phase synchronization effects of two linearly coupled chaotic Rössler oscillators.