An analytic framework for identifying finite-time coherent sets in time-dependent dynamical systems

PHYSICA D-NONLINEAR PHENOMENA

卷:250

Article

Froyland, Gary¹ 

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

关键词: Transfer operator;    Coherent set;    Finite-time dynamics;   

DOI  :  10.1016/j.physd.2013.01.013

来源: Elsevier

【 摘 要 】

The study of transport and mixing processes in dynamical systems is particularly important for the analysis of mathematical models of physical systems. Barriers to transport, which mitigate mixing, are currently the subject of intense study. In the autonomous setting, the use of transfer operators (Perron-Frobenius operators) to identify invariant and almost-invariant sets has been particularly successful. In the nonautonomous (time-dependent) setting, coherent sets, a time-parameterised family of minimally dispersive sets, are a natural extension of almost-invariant sets. The present work introduces a new analytic transfer operator construction that enables the calculation of finite-time coherent sets (sets are that minimally dispersive over a finite time interval). This new construction also elucidates the role of diffusion in the calculation and we show how properties such as the spectral gap and the regularity of singular vectors scale with noise amplitude. The construction can also be applied to general Markov processes on continuous state space. (C) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

Free