5 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…
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…
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…
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,…