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spatial Localization for Nonlinear Dynamical Stochastic Models for Excitable Media

Chinese Annals of Mathematics,Series B 2019年第6期40卷 891-924页

作者： Nan CHEN Andrew J.MAJDA Xin T.TONG Department of Mathematics University of Wisconsin-MadisonWI53705USA Department of Mathematics and Center for Atmosphere Ocean Science Courant Institute of Mathematical SciencesNew York UniversityNew YorkNY10012USA Center for Prototype Climate Modeling New York University AbuDhabiSaadiyat IslandAbuDhabiUAE Department of Mathematics National University of SingaporeSingapore 119076Singapore

Nonlinear dynamical stochastic models are ubiquitous in different *** statistical properties are often of great interest,but are also very challenging to *** excitable media models belong to such types of complex systems with large state dimensions and the associated covariance matrices have localized *** this article,a mathematical framework to understand the spatial localization for a large class of stochastically coupled nonlinear systems in high dimensions is *** mathematical analysis shows that the local effect from the diffusion results in an exponential decay of the components in the covariance matrix as a function of the distance while the global effect due to the mean field interaction synchronizes different components and contributes to a global *** analysis is based on a comparison with an appropriate linear surrogate model,of which the covariance propagation can be computed *** important applications of these theoretical results are *** are the spatial averaging strategy for efficiently sampling the covariance matrix and the localization technique in data *** examples of a linear model and a stochastically coupled Fitz Hugh-Nagumo model for excitable media are adopted to validate the theoretical *** latter is also used for a systematical study of the spatial averaging strategy in efficiently sampling the covariance matrix in different dynamical regimes.

关键词： Large state dimensions Diffusion Mean field interaction spatial averaging strategy Efficiently sampling

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