Topological Effects of Noise on Nonlinear Dynamics.

Summary Noise modifies the behavior of chaotic systems. Algebraic topology sheds light on the most fundamental effects involved, as illustrated herein by using the Lorenz (1963) model. This model's attractor is "strange" but frozen in time. When driven by multiplicative noise, the Lorenz model's random attractor (LORA) evolves in time. Here, we use Branched Manifold Analysis through Homologies (BraMAH) to describe LORA's coarse-grained topology. BraMAH is thus extended from deterministic flows to noise-driven systems. LORA's homology groups change in time and differ from the deterministic one.