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Continuous and discontinuous phase transitions and partial synchronization in stochastic three-state oscillators
Kevin Wood1, C Van den Broeck, R Kawai
1Department of Chemistry and Biochemistry and Institute for Nonlinear Science, University of California San Diego, 9500 Gilman Drive, La Jolla, California 92093-0340, USA.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 13, 2007
Summary
This study reveals that the transition to macroscopic synchronization in phase-coupled oscillators can be continuous or discontinuous, depending on coupling and disorder. It also uncovers a partial synchronization state where individual oscillator frequencies differ from the population
Area of Science:
- Physics
- Complex Systems
- Nonlinear Dynamics
Background:
- Macroscopic synchronization is a key phenomenon in various complex systems.
- Understanding the nature of transitions to synchronization is crucial for modeling collective behavior.
- Previous models often exhibit specific transition types, limiting generalizability.
Purpose of the Study:
- To investigate continuous and discontinuous transitions to macroscopic synchronization.
- To analyze the role of coupling coefficients and disorder in transition continuity.
- To explore the microscopic basis of synchronization and its relation to macroscopic observations.
Main Methods:
- Analytical investigation of discrete, stochastic, globally phase-coupled oscillators.
- Numerical simulations to provide evidence for analytical findings.
- Examination of time-averaged frequencies and mean-field oscillations.
Main Results:
- The continuity of the synchronization transition is dependent on coupling coefficients.
- Quenched disorder can influence transition continuity in nonuniform populations.
- A suprathreshold partial synchronization state was identified.
- Individual oscillator time-averaged frequencies may not match macroscopic oscillation frequencies in this state.
Conclusions:
- A simple model class exhibits diverse synchronization transition behaviors.
- The findings highlight counterintuitive subtleties in measuring synchronization dynamics.
- This work provides insights into the microscopic underpinnings of collective synchronization.
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