Centre for Modelling and Simulation, University of Pune, Pune 411007, India.
Chaos. 2013 Sep;23(3):033138. doi: 10.1063/1.4821916.
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.
我们研究了延迟圆映射。我们利用先前提出的延迟映射和时空系统之间的类比[F. T. Arecchi 等人，Phys. Rev. A 45, R4225 (1992)]来研究这个系统。在相图中，我们观察到层流相、行波缺陷相和驻波缺陷相。我们进一步推进了这个类比；在这个伪时空系统中，我们研究了“相”并定义了“序参量”来描述相之间的转变。我们发现，持续时间（定义为给定位置在时间 t 之前从未偏离过粗粒初始状态的概率）可以作为从行波相到驻波相转变的“序参量”。我们观察到在临界点以上存在有趣的有限“尺寸”标度和离临界标度。
