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Technical Report CMS-TR-20130919


Title Transition to almost periodic patterns in circle map with delay: Persistence as order parameter
Author/s Bhagat Lal Dutta
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 440033, India
Abstract We study delayed circle map. A previously proposed analogy between delayed map and spatiotemporal system [F. T. Arecchi et al., Phys. Rev. A 45, R4225 (1992)] is employed to study this system. In the phase diagram, we observe laminar phase, travelling defect phase, and standing defect phase. We push this analogy further; and in this pseudo-spatiotemporal system, we investigate “phases” and define “order parameter” to describe transition between phases. We find that persistence (defined as the probability that a given site has not deviated even once from its coarse grained initial state upto time t) works as an “order parameter” for the transition from a travelling wave phase to standing wave phase. We observe an interesting finite “size” scaling and off-critical scaling above the critical point.
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Citing This Document Bhagat Lal Dutta, and Prashant M. Gade , Transition to almost periodic patterns in circle map with delay: Persistence as order parameter . Technical Report CMS-TR-20130919 of the Centre for Modeling and Simulation, Savitribai Phule Pune University, Pune 411007, India (2013); available at http://cms.unipune.ernet.in/reports/.
Notes, Published Reference, Etc.
Contact bhagat AT cms.unipune.ernet.in
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