论文标题
1-dim混乱地图中的空间和颞泰勒定律
Spatial and Temporal Taylor's Law in 1-Dim Chaotic Maps
论文作者
论文摘要
通过使用低维混乱图，研究了称为泰勒定律（TL）的样本平均值和方差之间建立的功率定律关系。特别是，我们旨在阐明来自空间集合（STL）和暂时集合（TTL）的TL之间的关系。由于空间集合对应于固定分布的独立采样，因此我们确认STL是通过分布的偏度来解释的。 TTL和STL之间的差异显示为动力学的时间相关性。在有逻辑和帐篷图的情况下，分析发现了均值和方差中的二次关系，称为巴特利特定律。另一方面，Hassell模型中的TTL可以通过轨迹的块结构很好地解释，而Ricker模型的TTL具有不同的机制，源自地图的特定形式。
By using low-dimensional chaos maps, the power law relationship established between the sample mean and variance called Taylor's Law (TL) is studied. In particular, we aim to clarify the relationship between TL from the spatial ensemble (STL) and the temporal ensemble (TTL). Since the spatial ensemble corresponds to independent sampling from a stationary distribution, we confirm that STL is explained by the skewness of the distribution. The difference between TTL and STL is shown to be originated in the temporal correlation of a dynamics. In case of logistic and tent maps, the quadratic relationship in the mean and variance, called Bartlett's law, is found analytically. On the other hand, TTL in the Hassell model can be well explained by the chunk structure of the trajectory, whereas the TTL of the Ricker model have a different mechanism originated from the specific form of the map.
