439 citations · 769 across the 19 of their papers we have counts for
19 papers
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…
Dynamic solutions of next generation neural field models with delays
Oleh E. Omel'chenko, Carlo R. Laing
We study networks of theta neurons arranged on a ring with delayed interactions. In the continuum limit the systems are described by next generation neural field models with delays…
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…
Inverse problems for dynamic patterns in coupled oscillator networks: When larger networks are simpler
Oleh E. Omel'chenko
Networks of coupled phase oscillators are one of the most studied dynamical systems with numerous applications in physics, chemistry, biology, and engineering. Their behaviour is o…
Mechanisms for bump state localization in two-dimensional networks of leaky Integrate-and-Fire neurons
A. Provata, J. Hizanidis, K. Anesiadis +1
Networks of nonlocally coupled leaky Integrate-and-Fire neurons exhibit a variety of complex collective behaviors, such as partial synchronization, frequency or amplitude chimeras,…
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…
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…
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…
Bumps, chimera states, and Turing patterns in systems of coupled active rotators
Igor Franović, Oleh E. Omel'chenko, Matthias Wolfrum
Self-organized coherence-incoherence patterns, called chimera states, have first been reported in systems of Kuramoto oscillators. For coupled excitable units similar patterns, whe…
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…
Surfing the edge: using feedback control to find nonlinear solutions
Ashley P. Willis, Yohann Duguet, Oleh Omel'chenko +1
Many transitional wall-bounded shear flows are characterised by the coexistence in state-space of laminar and turbulent regimes. Probing the edge boundary between the two attractor…
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…
Regular and irregular patterns of self-localized excitation in arrays of coupled phase oscillators
Matthias Wolfrum, Oleh Omel'chenko, Jan Sieber
We study a system of phase oscillators with nonlocal coupling in a ring that supports self-organized patterns of coherence and incoherence, called chimera states. Introducing a glo…
Controlling unstable chaos: Stabilizing chimera states by feedback
Jan Sieber, Oleh Omel'chenko, Matthias Wolfrum
We present a control scheme that is able to find and stabilize an unstable chaotic regime in a system with a large number of interacting particles. This allows us to track a high d…
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…