Coherent sets for nonautonomous dynamical systems

PHYSICA D-NONLINEAR PHENOMENA

卷:239

Article

Froyland, Gary¹  Lloyd, Simon¹  Santitissadeekorn, Naratip¹ 

[1] Univ New S Wales, Sch Math & Stat, Sydney, NSW 2052, Australia

关键词: Perron-Frobenius operator;    Coherent set;    Nonautonomous dynamical system;    Oseledets subspace;    Lyapunov exponent;    Almost-invariant set;    Metastable set;    Strange eigenmode;    Persistent pattern;   

DOI  :  10.1016/j.physd.2010.03.009

来源: Elsevier

【 摘 要 】

We describe a mathematical formalism and numerical algorithms for identifying and tracking slowly mixing objects in nonautonomous dynamical systems. In the autonomous setting, such objects are variously known as almost-invariant sets, metastable sets, persistent patterns, or strange eigenmodes, and have proved to be important in a variety of applications. In this current work, we explain how to extend existing autonomous approaches to the nonautonomous setting. We call the new time-dependent slowly mixing objects coherent sets as they represent regions of phase space that disperse very slowly and remain coherent. The new methods are illustrated via detailed examples in both discrete and continuous time. (C) 2010 Elsevier B.V. All rights reserved.

【 授权许可】

Free