Center for Modeling and Simulation, University of Pune, Pune 411 007, India.
Chaos. 2011 Mar;21(1):013122. doi: 10.1063/1.3556683.
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.
我们研究了存在反馈的耦合圆映射，并探索了在这个耦合高维映射系统中观察到的各种动力学相。我们观察到从局域混沌到时空混沌的有趣转变。我们将这个转变作为动态相变来研究。我们观察到，持续度作为一个极好的量化指标来描述这个转变。我们以圆映射的不动点的位置（不受反馈影响）作为参考点，计算在时间 t 之前已经大于（小于）不动点的站点数量。尽管在这种情况下局部动力学是高维的，但这种跟踪单个变量的持续度定义是这个转变的一个极好的量化指标。在大多数情况下，我们在临界点也获得了一个定义良好的持续度指数，并观察到了类似于二阶相变的常规标度。这表明，持续度可以作为从完全或部分被阻止的相转变的良好的序参量。我们还对局域态的雅可比行列式的特征值谱中的间隙给出了解释。
