Neuromodulatory effects on synchrony and network reorganization in networks of coupled Kuramoto oscillators.

Neuromodulatory processes in the brain can critically change signal processing on a cellular level, leading to dramatic changes in network level reorganization. Here, we use coupled nonidentical Kuramoto oscillators to investigate how changes in the shape of phase response curves from Type 1 to Type 2, mediated by varying ACh levels, coupled with activity-dependent plasticity may alter network reorganization. We first show that, when plasticity is absent, the Type 1 networks with symmetric adjacency matrix, as expected, exhibit asynchronous dynamics with oscillators of the highest natural frequency robustly evolving faster in terms of their phase dynamics. However, interestingly, Type 1 networks with an asymmetric connectivity matrix can produce stable synchrony (so-called splay states) with complex phase relationships. At the same time, Type 2 networks synchronize independent of the symmetry of their connectivity matrix, with oscillators locked so that those with higher natural frequency have a constant phase lead as compared to those with lower natural frequency. This relationship establishes a robust mapping between the frequency and oscillators' phases in the network, leading to structure and frequency mapping when plasticity is present. Finally, we show that biologically realistic, phase-locking dependent, connection plasticity naturally produces splay states in Type 1 networks that do not display the structure-frequency reorganization observed in synchronized Type II networks. These results indicate that the formation of splay states in the brain could be a common phenomenon.