Charó Gisela D, Chekroun Mickaël D, Sciamarella Denisse, Ghil Michael
CONICET-Universidad de Buenos Aires, Centro de Investigaciones del Mar y la Atmósfera (CIMA), C1428EGA Ciudad Autónoma de Buenos Aires, Argentina.
Weizmann Institute of Science, Rehovot 7610001, Israel.
Chaos. 2021 Oct;31(10):103115. doi: 10.1063/5.0059461.
Noise modifies the behavior of chaotic systems in both quantitative and qualitative ways. To study these modifications, the present work compares the topological structure of the deterministic Lorenz (1963) attractor with its stochastically perturbed version. The deterministic attractor is well known to be "strange" but it is frozen in time. When driven by multiplicative noise, the Lorenz model's random attractor (LORA) evolves in time. Algebraic topology sheds light on the most striking effects involved in such an evolution. In order to examine the topological structure of the snapshots that approximate LORA, we use branched manifold analysis through homologies-a technique originally introduced to characterize the topological structure of deterministically chaotic flows-which is being extended herein to nonlinear noise-driven systems. The analysis is performed for a fixed realization of the driving noise at different time instants in time. The results suggest that LORA's evolution includes sharp transitions that appear as topological tipping points.
噪声在定量和定性方面都会改变混沌系统的行为。为了研究这些改变，本研究将确定性的洛伦兹（1963）吸引子的拓扑结构与其随机扰动版本进行了比较。确定性吸引子是众所周知的“奇怪”吸引子，但它在时间上是固定的。当由乘性噪声驱动时，洛伦兹模型的随机吸引子（LORA）会随时间演化。代数拓扑揭示了这种演化中涉及的最显著的效应。为了研究近似LORA的快照的拓扑结构，我们通过同调进行分支流形分析——这是一种最初用于刻画确定性混沌流拓扑结构的技术——本文将其扩展到非线性噪声驱动系统。针对驱动噪声在不同时刻的固定实现进行分析。结果表明，LORA的演化包括作为拓扑临界点出现的急剧转变。
