Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2009-03-27
Phys. Rev. E 79, 016112 (2009)
Physics
Condensed Matter
Disordered Systems and Neural Networks
22 pages, 5 figures
Scientific paper
10.1103/PhysRevE.79.016112
The Kuramoto phase diffusion equation is a nonlinear partial differential equation which describes the spatio-temporal evolution of a phase variable in an oscillatory reaction diffusion system. Synchronization manifests itself in a stationary phase gradient where all phases throughout a system evolve with the same velocity, the synchronization frequency. The formation of concentric waves can be explained by local impurities of higher frequency which can entrain their surroundings. Concentric waves in synchronization also occur in heterogeneous systems, where the local frequencies are distributed randomly. We present a perturbation analysis of the synchronization frequency where the perturbation is given by the heterogeneity of natural frequencies in the system. The nonlinearity in form of dispersion, leads to an overall acceleration of the oscillation for which the expected value can be calculated from the second order perturbation terms. We apply the theory to simple topologies, like a line or the sphere, and deduce the dependence of the synchronization frequency on the size and the dimension of the oscillatory medium. We show that our theory can be extended to include rotating waves in a medium with periodic boundary conditions. By changing a system parameter the synchronized state may become quasi degenerate. We demonstrate how perturbation theory fails at such a critical point.
Blasius Bernd
Toenjes Ralf
No associations
LandOfFree
Perturbation Analysis of the Kuramoto Phase Diffusion Equation Subject to Quenched Frequency Disorder does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Perturbation Analysis of the Kuramoto Phase Diffusion Equation Subject to Quenched Frequency Disorder, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Perturbation Analysis of the Kuramoto Phase Diffusion Equation Subject to Quenched Frequency Disorder will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-21243