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| Title | Dynamic Phase Transition from Localized to Spatiotemporal Chaos in Coupled Circle Map with Feedback |
| Author/s |
Abhijeet R. Sonawane
Centre for Modeling and Simulation, Savitribai Phule Pune University, Pune 411 007 India Prashant M. Gade PG Department of Physics, Rashtrasant Tukdoji Maharaj Nagpur University, Nagpur 440 033 India |
| Abstract | We investigate coupled circle maps in presence of feedback and explore various dynamical phases observed in this system of coupled high dimensional maps. We observe an interesting transition from localized chaos to spatiotemporal chaos. We study this transition as a dynamic phase transition. We observe that persistence acts as an excellent quantifier to describe this transition. Taking the location of the fixed point of circle map (which does not change with feedback) as a reference point, we compute number of sites which have been greater than (less than) the fixed point till time t. Though local dynamics is high-dimensional in this case this definition of persistence which tracks a single variable is an excellent quantifier for this transition. In most cases, we also obtain a well defined persistence exponent at the critical point and observe conventional scaling as seen in second order phase transitions. This indicates that persistence could work as good order parameter for transitions from fully or partially arrested phase. We also give an explanation of gaps in eigenvalue spectrum of the Jacobian of localized state. |
| Keywords | |
| Download | arXiv • Journal |
| Citing This Document | Abhijeet R. Sonawane, and Prashant M. Gade , Dynamic Phase Transition from Localized to Spatiotemporal Chaos in Coupled Circle Map with Feedback . Technical Report CMS-TR-20110221 of the Centre for Modeling and Simulation, Savitribai Phule Pune University, Pune 411007, India (2011); available at http://cms.unipune.ac.in/reports/. |
| Notes, Published Reference, Etc. | Published as Chaos 21, 013122 (2011). |
| Contact | abhijeetrs AT gmail.com |
| Supplementary Material |