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 non-identical 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, as expected, exhibit asynchronous dynamics with oscillators of the highest natural frequency robustly evolving faster in terms of their phase dynamics. At the same time, the Type 2 networks synchronize, with oscillators locked so that the ones with higher natural frequency have a constant phase lead as compared to the ones with lower natural frequency. This relationship establishes a robust mapping between the frequency and oscillators' phases in the network, leading to structure/frequency mapping when plasticity is present. Further we show that while connection plasticity can produce stable synchrony (so called splay states) in Type 1 networks, the structure/frequency reorganization observed in Type 2 networks is not present.