Topology, vorticity, and limit cycle in a stabilized Kuramoto–Sivashinsky equation

Autor:	Yong-Cong Chen, Chunxiao Shi, J. M. Kosterlitz, Xiaomei Zhu, Ping Ao
Rok vydání:	2022
Předmět:	Diffusion Motion Multidisciplinary FOS: Physical sciences Neural Networks Computer Pattern Formation and Solitons (nlin.PS) Nonlinear Sciences - Pattern Formation and Solitons Adaptation and Self-Organizing Systems (nlin.AO) Nonlinear Sciences - Adaptation and Self-Organizing Systems
Zdroj:	Proceedings of the National Academy of Sciences. 119
ISSN:	1091-6490 0027-8424
Popis:	A noisy stabilized Kuramoto-Sivashinsky equation is analyzed by stochastic decomposition. For values of control parameter for which periodic stationary patterns exist, the dynamics can be decomposed into diffusive and transverse parts which act on a stochastic potential. The relative positions of stationary states in the stochastic global potential landscape can be obtained from the topology spanned by the low-lying eigenmodes which inter-connect them. Numerical simulations confirm the predicted landscape. The transverse component also predicts a universal class of vortex like circulations around fixed points. These drive nonlinear drifting and limit cycle motion of the underlying periodic structure in certain regions of parameter space. Our findings might be relevant in studies of other nonlinear systems such as deep learning neural networks. Comment: Main body: 16 pages, 3 figures; Supplementary: 14 pages, 6 figures
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b26ca9540482afead87cf3b4b128f38e https://doi.org/10.1073/pnas.2211359119 Zobrazit plný text záznamu