Dynamic Phase Transition from Localized to Spatiotemporal Chaos in Coupled Circle Map with Feedback

TL;DR

This paper studies a transition from localized chaos to spatiotemporal chaos in coupled circle maps with feedback, using persistence as a key quantifier, revealing critical scaling behavior similar to second order phase transitions.

Contribution

It introduces persistence as an effective order parameter for phase transitions in high-dimensional coupled maps with feedback, and characterizes the critical behavior of this transition.

Findings

Persistence exponent is well-defined at the critical point.

The transition exhibits conventional scaling akin to second order phase transitions.

Eigenvalue spectrum gaps are explained in the context of localized states.

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.