- Series
- CDSNS Colloquium
- Time
- Monday, January 6, 2014 - 11:00am for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- James Meiss* – Department of Applied Mathematics, University of Colorado, Boulder
- Organizer
- Adam Fox
Synchronization of coupled oscillators, such as grandfather clocks or
metronomes, has been much studied using the approximation of strong
damping in which case the dynamics of each reduces to a phase on a limit
cycle. This gives rise to the famous Kuramoto model. In contrast, when
the oscillators are Hamiltonian both the amplitude and phase of each
oscillator are dynamically important. A model in which all-to-all
coupling is assumed, called the Hamiltonian Mean Field (HMF) model, was
introduced by Ruffo and his colleagues. As for the Kuramoto model, there
is a coupling strength threshold above which an incoherent state loses
stability and the oscillators synchronize.
We study the case when the moments of inertia and coupling strengths of
the oscillators are heterogeneous. We show that finite size fluctuations
can greatly modify the synchronization threshold by inducing
correlations between the momentum and parameters of the rotors. For
unimodal parameter distributions, we find an analytical expression for
the modified critical coupling strength in terms of statistical
properties of the parameter distributions and confirm our results with
numerical simulations. We find numerically that these effects disappear
for strongly bimodal parameter distributions.
*This work is in collaboration with Juan G. Restrepo.