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arXiv · 2409.02498

Noise-induced order in high dimensions

Huayan Chen·Yuzuru Sato
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Abstract

Noise-induced phenomena in high-dimensional dynamical systems were investigated from a random dynamical systems point of view. In a class of generalized H\'enon maps, which are randomly perturbed delayed logistic maps, with monotonically increasing noise levels, we observed (i) an increase in the number of positive Lyapunov exponents from 4 to 5, and the emergence of characteristic periods at the same time, and (ii) a decrease in the number of positive Lyapunov exponents from 4 to 3, and an increase in Kolmogorov--Sinai entropy at the same time. Our results imply that simple concepts of noise-induced phenomena, such as noise-induced chaos and/or noise-induced order, may not describe those analogue in high dimensional dynamical systems, owing to coexistence of noise-induced chaos and noise-induced order.

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Huayan Chen, Yuzuru Sato. 2024-09-04. Noise-induced order in high dimensions. https://arxiv.org/abs/2409.02498

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