439 citations · 769 across the 19 of their papers we have counts for
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Hopf Bifurcations of Twisted States in Phase Oscillators Rings with Nonpairwise Higher-Order Interactions
Christian Bick, Tobias Böhle, Oleh E. Omel'chenko
Synchronization is an essential collective phenomenon in networks of interacting oscillators. Twisted states are rotating wave solutions in ring networks where the oscillator phase…
Chimera states emerging from dynamical trapping in chaotic saddles
Everton S. Medeiros, Oleh Omel'chenko, Ulrike Feudel
Nonlinear systems possessing nonattracting chaotic sets, such as chaotic saddles, embedded in their state space may oscillate chaotically for a transient time before eventually tra…
Periodic solutions in next generation neural field models
Carlo R. Laing, Oleh E. Omel'chenko
We consider a next generation neural field model which describes the dynamics of a network of theta neurons on a ring. For some parameters the network supports stable time-periodic…