439 citations · 769 across the 19 of their papers we have counts for
10 papers · 1 filter
Cluster dynamics in a two-group Stuart-Landau model analyzed by the second-order phase reduction
Yernur Baibolatov, Oleh E. Omel'chenko, Michael Rosenblum
We analyze cluster states in an ensemble of Stuart-Landau oscillators with two subpopulations of different frequencies. Our main goal is to compare the descriptions of the system's…
Mean-field approach to finite-size fluctuations in the Kuramoto-Sakaguchi model
Oleh E. Omel'chenko, Georg A. Gottwald
We develop an ab initio approach to describe the statistical behavior of finite-size fluctuations in the deterministic Kuramoto-Sakaguchi model. We obtain explicit expressions for…
Activity patterns in ring networks of quadratic integrate-and-fire neurons with synaptic and gap junction coupling
Oleh E. Omel'chenko, Carlo R. Laing
We consider a ring network of quadratic integrate-and-fire neurons with nonlocal synaptic and gap junction coupling. The corresponding neural field model supports solutions such as…
Phase reduction explains chimera shape: when multi-body interaction matters
Erik T. K. Mau, Oleh E. Omel'chenko, Michael Rosenblum
We present an extension of the Kuramoto-Sakaguchi model for networks, deriving the second-order phase approximation for a paradigmatic model of oscillatory networks - an ensemble o…
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…
Periodic orbits in the Ott-Antonsen manifold
Oleh Omel'chenko
In their seminal paper [Chaos 18, 037113 (2008)], E. Ott and T. M. Antonsen showed that large groups of phase oscillators driven by a certain type of common force display low dimen…
Mathematical framework for breathing chimera states
Oleh Omel'chenko
About two decades ago it was discovered that systems of nonlocally coupled oscillators can exhibit unusual symmetry-breaking patterns composed of coherent and incoherent regions. S…
Moving bumps in theta neuron networks
Carlo R. Laing, Oleh Omel'chenko
We consider large networks of theta neurons on a ring, synaptically coupled with an asymmetric kernel. Such networks support stable "bumps" of activity, which move along the ring i…
A Tweezer for Chimeras in Small Networks
Iryna Omelchenko, Oleh E. Omel'chenko, Anna Zakharova +2
We propose a control scheme which can stabilize and fix the position of chimera states in small networks. Chimeras consist of coexisting domains of spatially coherent and incoheren…
When Nonlocal Coupling Between Oscillators Becomes Stronger: Patched Synchrony or Multi-Chimera States
Iryna Omelchenko, Oleh E. Omel'chenko, Philipp Hövel +1
Systems of nonlocally coupled oscillators can exhibit complex spatio-temporal patterns, called chimera states, which consist of coexisting domains of spatially coherent (synchroniz…