Related Experiment Video
Updated: Aug 18, 2026

Optogenetic Entrainment of Hippocampal Theta Oscillations in Behaving Mice
Published on: June 29, 2018
Onset of synchronization in large networks of coupled oscillators
Juan G Restrepo1, Edward Ott, Brian R Hunt
1Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, MD 20742, USA. juanga@math.umd.edu
Abstract:
We study the transition from incoherence to coherence in large networks of coupled phase oscillators. We present various approximations that describe the behavior of an appropriately defined order parameter past the transition and generalize recent results for the critical coupling strength. We find that, under appropriate conditions, the coupling strength at which the transition occurs is determined by the largest eigenvalue of the adjacency matrix. We show how, with an additional assumption, a mean-field approximation recently proposed is recovered from our results. We test our theory with numerical simulations and find that it describes the transition when our assumptions are satisfied. We find that our theory describes the transition well in situations in which the mean-field approximation fails. We study the finite-size effects caused by nodes with small degree and find that they cause the critical coupling strength to increase.
Related Concept Videos
Oscillations In An LC Circuit
Forced Oscillations
Damped Oscillations
Although friction and other non-conservative...
Oscillations about an Equilibrium Position
¹H NMR: Interpreting Distorted and Overlapping Signals
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are slanted or...
RLC Circuit as a Damped Oscillator
Consider a series RLC circuit. Here, the presence of resistance in the circuit leads to energy loss due to joule heating in the resistance. Therefore, the total electromagnetic energy in the circuit is no longer constant and decreases with time. Since the magnitude of charge, current, and potential difference continuously decreases, their oscillations are said to be damped. This is...

