Mutual information resonances in delay-coupled limit cycle and quasi-cycle brain rhythms.

We elucidate how coupling delays and noise impact phase and mutual information relationships between two stochastic brain rhythms. This impact depends on the dynamical regime of each PING-based rhythm, as well as on network heterogeneity and coupling asymmetry. The number of peaks at positive and negative time lags in the delayed mutual information between the two bi-directionally communicating rhythms defines our measure of flexibility of information sharing and reflects the number of ways in which the two networks can alternately lead one another. We identify two distinct mechanisms for the appearance of qualitatively similar flexible information sharing. The flexibility in the quasi-cycle regime arises from the coupling delay-induced bimodality of the phase difference distribution, and the related bimodal mutual information. It persists in the presence of asymmetric coupling and heterogeneity but is limited to two routes of information sharing. The second mechanism in noisy limit cycle regime is not induced by the delay. However, delay-coupling and heterogeneity enable communication routes at multiple time lags. Noise disrupts the shared compromise frequency, allowing the expression of individual network frequencies which leads to a slow beating pattern. Simulations of an envelope-phase description for delay-coupled quasi-cycles yield qualitatively similar properties as for the full system. Near the bifurcation from in-phase to out-of-phase behaviour, a single preferred phase difference can coexist with two information sharing routes; further, the phase laggard can be the mutual information leader, or vice versa. Overall, the coupling delay endows a two-rhythm system with an array of lead-lag relationships and mutual information resonances that exist in spite of the noise and across the Hopf bifurcation. These beg to be mapped out experimentally with the help of our predictions.