Synchronization of Phase Oscillators on the Hierarchical Lattice
@article{Garlaschelli2017SynchronizationOP, title={Synchronization of Phase Oscillators on the Hierarchical Lattice}, author={Diego Garlaschelli and Frank den Hollander and Janusz M. Meylahn and Benthen Zeegers}, journal={Journal of Statistical Physics}, year={2017}, volume={174}, pages={188-218} }
Synchronization of neurons forming a network with a hierarchical structure is essential for the brain to be able to function optimally. In this paper we study synchronization of phase oscillators on the most basic example of such a network, namely, the hierarchical lattice. Each site of the lattice carries an oscillator that is subject to noise. Pairs of oscillators interact with each other at a strength that depends on their hierarchical distance, modulated by a sequence of interaction…
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References
SHOWING 1-10 OF 23 REFERENCES
Biological rhythms and the behavior of populations of coupled oscillators.
- BiologyJournal of theoretical biology
- 1967
The Kuramoto model: A simple paradigm for synchronization phenomena
- Physics
- 2005
Synchronization phenomena in large populations of interacting elements are the subject of intense research efforts in physical, biological, chemical, and social systems. A successful approach to the…
Stability of incoherence in a population of coupled oscillators
- Physics, Mathematics
- 1991
We analyze a mean-field model of coupled oscillators with randomly distributed frequencies. This system is known to exhibit a transition to collective oscillations: for small coupling, the system is…
Long time dynamics and disorder-induced traveling waves in the stochastic Kuramoto model
- Mathematics
- 2015
The aim of the paper is to address the long time behavior of the Kuramoto model of mean-field coupled phase rotators, subject to white noise and quenched frequencies. We analyse the influence of the…
Long time behavior of a spherical mean field model
- Mathematics
- 2002
In this thesis, we study some aspects of the long time behavior of a spherical mean field model. This model is motivated by problems in mathematical physics and statistical mechanics. More precisely,…
Coupled nonlinear oscillators below the synchronization threshold: Relaxation by generalized Landau damping.
- PhysicsPhysical review letters
- 1992
This work analyzes a model of globally coupled nonlinear oscillators with randomly distributed frequencies and proves that, for coupling strengths below a certain threshold, this system would always relax to an incoherent state.
Approximate solution to the stochastic Kuramoto model.
- MathematicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2013
The Kuramoto phase oscillators can be reduced in a Gaussian approximation to two first-order differential equations to yield a solution for the time-dependent order parameter, which characterizes the synchronization between the oscillators.
Cooperative Phenomena in Coupled Oscillator Systems under External Fields
- Physics
- 1988
Systems of many limit cycle oscillators are studied by using a phase description of the oscillation. Each oscillator interacts with all the other oscillators uniformly and is subject to external…