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We investigate coupled circle maps in presence of feedback and explorevarious dynamical phases observed in this system of coupled high dimensionalmaps. We observe an interesting transition from localized chaos tospatiotemporal chaos. We study this transition as a dynamic phase transition.We observe that persistence acts as an excellent quantifier to describe thistransition. Taking the location of the fixed point of circle map (which doesnot change with feedback) as a reference point, we compute number of siteswhich have been greater than (less than) the fixed point till time t. Thoughlocal dynamics is high-dimensional in this case this definition of persistencewhich tracks a single variable is an excellent quantifier for this transition.In most cases, we also obtain a well defined persistence exponent at thecritical point and observe conventional scaling as seen in second order phasetransitions. This indicates that persistence could work as good order parameterfor transitions from fully or partially arrested phase. We also give anexplanation of gaps in eigenvalue spectrum of the Jacobian of localized state.

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