Hiroki Kojima, Yuzuru Mitsui and Takashi Ikegami
URL: https://pubs.aip.org/aip/cha/article/31/3/033111/342146/
arXiv: https://arxiv.org/abs/2009.13417
Original Abstract: By using low-dimensional chaotic 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 sample 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 has a different mechanism originated from the specific form of the map.
Summary (EN): Studies Taylor's Law (a power-law relationship between sample mean and variance) in low-dimensional chaotic maps, clarifying the link between its spatial (STL) and temporal (TTL) forms. STL is explained by the skewness of the distribution, while the STL–TTL difference originates in temporal correlation of the dynamics; Bartlett's law is derived analytically for logistic and tent maps, with distinct mechanisms for the Hassell and Ricker models.
概要（日本語）: 低次元カオス写像を用い、標本平均と分散の間に成り立つべき乗則「テイラー則（TL）」を研究。空間アンサンブル由来のTL（STL）と時間アンサンブル由来のTL（TTL）の関係を明らかにし、STLは分布の歪度で説明できること、両者の差は力学の時間相関に起因することを示す。ロジスティック写像・テント写像では平均と分散の2次関係（Bartlett則）を解析的に導出。Hasselモデルとは異なり、Rickerモデルでは別の機構が働く。
