Zobrazeno 1 - 10
of 102
pro vyhledávání: '"Omel'chenko, Oleh"'
Autor:
Omel'chenko, Oleh E., Laing, Carlo R.
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 standing and travelling waves, and also lurching waves. We show that
Externí odkaz:
http://arxiv.org/abs/2406.01881
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 of non-identical Stuart-Landau oscillators coupled pairwisely via an ar
Externí odkaz:
http://arxiv.org/abs/2401.05366
Publikováno v:
Journal of Physics: Complexity, 5:025026, 2024
Synchronization is an essential collective phenomenon in networks of interacting oscillators. Twisted states are rotating wave solutions in ring networks where the oscillator phases wrap around the circle in a linear fashion. Here, we analyze Hopf bi
Externí odkaz:
http://arxiv.org/abs/2310.15698
Nonlinear systems possessing nonattracting chaotic sets, such as chaotic saddles, embedded in their state space may oscillate chaotically for a transient time before eventually transitioning into some stable attractor. We show that these systems, whe
Externí odkaz:
http://arxiv.org/abs/2307.06918
Autor:
Laing, Carlo R., Omel'chenko, Oleh E.
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 solutions. Using the fact that the dynamics at each spatial location
Externí odkaz:
http://arxiv.org/abs/2306.10398
Autor:
Omel'chenko, Oleh
Publikováno v:
Nonlinearity 36, 845 (2023)
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 dimensional long-term dynamics, which is described by a small number of ord
Externí odkaz:
http://arxiv.org/abs/2206.01481
Autor:
Omel'chenko, Oleh
Publikováno v:
J. Nonlinear Sci. 32:22 (2022)
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. Since then such patterns, called chimera states, have been the subject
Externí odkaz:
http://arxiv.org/abs/2111.14555
Publikováno v:
Phys. Rev. E 104, L052201 (2021)
Self-organized coherence-incoherence patterns, called chimera states, have first been reported in systems of Kuramoto oscillators. For coupled excitable units similar patterns, where coherent units are at rest, are called bump states. Here, we study
Externí odkaz:
http://arxiv.org/abs/2104.03025
Autor:
Laing, Carlo R., Omel'chenko, Oleh
Publikováno v:
Chaos 30, 043117 (2020)
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 if the coupling kernel is asymmetric. We investigate the effects of the
Externí odkaz:
http://arxiv.org/abs/2004.00699
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