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Tiered synchronization in coupled oscillator populations with interaction delays and higher-order interactions
Per Sebastian Skardal1, Can Xu2
1Department of Mathematics, Trinity College, Hartford, Connecticut 06106, USA.
Abstract:
We study synchronization in large populations of coupled phase oscillators with time delays and higher-order interactions. With each of these effects individually giving rise to bistability between incoherence and synchronization via subcriticality at the onset of synchronization and the development of a saddle node, we find that their combination yields another mechanism behind bistability, where supercriticality at onset may be maintained; instead, the formation of two saddle nodes creates tiered synchronization, i.e., bistability between a weakly synchronized state and a strongly synchronized state. We demonstrate these findings by first deriving the low dimensional dynamics of the system and examining the system bifurcations using a stability and steady-state analysis.
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