Phase locking of pulse-coupled oscillators with delays is determined by the phase response curve

Abstract

Event Abstract Back to Event Phase locking of pulse-coupled oscillators with delays is determined by the phase response curve Gamma oscillations (30-70 Hz) can synchronize with near zero phase lag over multiple cortical regions and between hemispheres, and between two distal sites in hippocampal slices in which gamma was induced by tetanus. Additionally, oscillations the gamma band can synchronize with nonzero phase lag between pairs of EEG electrodes. There are two mechanisms by which long range synchronization could occur: by locking to a common input or via reciprocal coupling. Here we address phase-locking that arises via bidirectional coupling of two limit cycle oscillators with a conduction delay. It is often implied that for two distal oscillators, phase lags equal to the conduction delay are expected, and how synchronization can take place over long distances in a stable manner is considered an open question. Here we assume that under conditions in which two local circuit generators of gamma oscillations arise separated by some distance, these circuits function as intrinsic nonlinear oscillators that are bidirectionally coupled with a conduction delay. Nothing is assumed regarding the oscillators other than that the phase response curve (PRC) can be measured using an input that approximates the one received from the other oscillator, and that the effect of the coupling is dissipated within one network period such that the coupling is effectively pulsatile. Here we derive existence and stability criteria based on the PRC for phase locking with delays of any length, and test them on oscillators with a wide variety of PRCs and varying levels of heterogeneity. The method is accurate for any shape PRC that we examined and therefore very general. For identical frequencies, identical coupling strength, and identical delays, synchrony emerges as a consequence of symmetry. We show that for both homogenous and heterogenous networks, in phase synchronization alternates with out of phase synchronization as the delay is increased, with regions of bistability in the intermediate values. In practice, the frequencies of the local circuits are unlikely to be identical; therefore, the cycle periods need to be altered via phase resetting in order to reach a common frequency. If the coupling is strong, as it must be in order for synchronization to occur rapidly, and the frequencies, conduction delays and PRCs of the oscillators are similar, then the input to each neuron will arrive at a similar phase, resulting in a small phase lag in the firing times. The stability of the phase locking depends upon the slope of the phase resetting curve at the phase at which the input is received in the phase locked mode. In other circuits, the conduction delays are asymmetric, in which case additional mechanisms may be required to achieve near zero phase lag. Having an explicit and general solution for the existence and stability of in phase locking with delay can provide insight into how such locking is achieved in the brain. Conference: Computational and systems neuroscience 2009, Salt Lake City, UT, United States, 26 Feb - 3 Mar, 2009. Presentation Type: Poster Presentation Topic: Poster Presentations Citation: (2009). Phase locking of pulse-coupled oscillators with delays is determined by the phase response curve. Front. Syst. Neurosci. Conference Abstract: Computational and systems neuroscience 2009. doi: 10.3389/conf.neuro.06.2009.03.139 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 02 Feb 2009; Published Online: 02 Feb 2009. Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers Google Google Scholar PubMed Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.