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Synchronization of oscillators with long-range power law interactions
Debanjan Chowdhury1, M C Cross
1Department of Physics, California Institute of Technology, Pasadena, California 91125, USA. debanjanchowdhury@gmail.com
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 28, 2010
Summary
We found a critical exponent of 3/2 for synchronized oscillators with power law interactions. This exponent governs the transition between synchronized and unsynchronized states in one-dimensional systems.
Area of Science:
- Physics
- Statistical Mechanics
- Complex Systems
Background:
- Oscillator synchronization is crucial in various natural and engineered systems.
- Long-range interactions significantly influence collective dynamics.
Purpose of the Study:
- To investigate the synchronization transition in a one-dimensional lattice of oscillators with power law interactions.
- To determine the critical exponent governing this transition.
Main Methods:
- Analytical calculations using spin-wave approximation.
- Numerical simulations.
- Coarse-graining approach.
Main Results:
- Identified a critical power law exponent α(c) = 3/2 for synchronization.
- Observed a transition from synchronized to unsynchronized states at α(c).
- Analyzed frequency entrainment and phase ordering for α ≥ 1.
Conclusions:
- The critical exponent α(c) = 3/2 dictates synchronization in 1D systems with power law interactions.
- Results generalize to d-dimensional systems.
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