2011/01/25 by Abhijeet R. Sonawane, Prashant M. Gade
Computer Science · Physics and Astronomy · #Chaos control and synchronization #Chaotic #Critical point (mathematics) #Eigenvalues and eigenvectors #Fixed point #Hénon map #Jacobian matrix and determinant #Nonlinear Dynamics and Pattern Formation #Persistence (discontinuity) #Phase (matter) #Phase transition #Quantum chaos and dynamical systems #Scaling #nlin.CD
paper · pdf · doi:10.1063/1.3556683
published as CHAOS 21, 013122 (2011)
arxiv created 2011/01/25 · openalex publication_date 2011/03/01 · arxiv updated 2015/03/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We investigate coupled circle maps in the 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 a number of sites which have been greater than (less than) the fixed point until 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 a 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.