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Dynamic phase transition from localized to spatiotemporal chaos in coupled circle map with feedback
Abhijeet R Sonawane1, Prashant M Gade
1Center for Modeling and Simulation, University of Pune, Pune 411 007, India. abhijeetrs@gmail.com
Chaos (Woodbury, N.Y.)
|April 5, 2011
Summary
We found that persistence quantifies dynamic phase transitions in coupled circle maps, moving from localized to spatiotemporal chaos. This method reveals conventional scaling, similar to second-order phase transitions.
Area of Science:
- Complex Systems
- Nonlinear Dynamics
- Statistical Physics
Background:
- Coupled circle maps exhibit complex behaviors, including various dynamical phases.
- Understanding transitions between these phases, such as localized to spatiotemporal chaos, is crucial.
Purpose of the Study:
- To investigate dynamic phase transitions in coupled circle maps with feedback.
- To identify effective quantifiers for transitions from localized to spatiotemporal chaos.
Main Methods:
- Analyzing coupled high-dimensional circle maps with feedback.
- Employing persistence as a quantifier, tracking deviations from a fixed point.
- Calculating persistence exponents and observing scaling behavior.
Main Results:
- A clear transition from localized chaos to spatiotemporal chaos was observed.
- Persistence effectively quantifies this dynamic phase transition.
- Conventional scaling, characteristic of second-order phase transitions, was identified at the critical point.
Conclusions:
- Persistence serves as a robust order parameter for dynamic phase transitions in this system.
- The findings suggest persistence can characterize transitions from arrested phases.
- Eigenvalue spectrum gaps in localized states were also explained.
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