论文标题
在开放系统中有限时期瞬态混乱的本地表征
Local characterization of transient chaos on finite times in open systems
论文作者
论文摘要
为了表征与开放动力学系统中与瞬态混乱相关的局部有限时间属性，我们在粗粒的描述中引入了适合此目的的逃生速率和分形维度。我们从数值上说明这些量词在动力学的整个域上具有相当大的分布，但是它们的空间变化，尤其是在长而非反对的积分时间上，与坎茨和格拉伯格在临时渐近量化的情况下认识到的关系大致相一致。特别是，与这种关系的偏差小于各个位置之间的差异，这证实了这种动力学定律的存在以及我们的量化器对代表非反应性制度中潜在动力学特性的适用性。
To characterize local finite-time properties associated with transient chaos in open dynamical systems, we introduce an escape rate and fractal dimensions suitable for this purpose in a coarse-grained description. We numerically illustrate that these quantifiers have a considerable spread across the domain of the dynamics, but their spatial variation, especially on long but non-asymptotic integration times, is approximately consistent with the relationship that was recognized by Kantz and Grassberger for temporally asymptotic quantifiers. In particular, deviations from this relationship are smaller than differences between various locations, which confirms the existence of such a dynamical law and the suitability of our quantifiers to represent underlying dynamical properties in the non-asymptotic regime.
