A method for revealing phase space structures of general time dependent dynamical systems

Mancho, Ana María and Wiggins, Stephen and Curbelo, Jezabel and Mendoza Parra, Carolina Andrea (2013). A method for revealing phase space structures of general time dependent dynamical systems. "Communications in Nonlinear Science and Numerical Simulation", v. 18 (n. 12); pp. 3530-3557. ISSN 1007-5704. https://doi.org/10.1016/j.cnsns.2013.05.002.

Description

Title: A method for revealing phase space structures of general time dependent dynamical systems
Author/s:
  • Mancho, Ana María
  • Wiggins, Stephen
  • Curbelo, Jezabel
  • Mendoza Parra, Carolina Andrea
Item Type: Article
Título de Revista/Publicación: Communications in Nonlinear Science and Numerical Simulation
Date: November 2013
ISSN: 1007-5704
Volume: 18
Subjects:
Freetext Keywords: Invariant manifolds, nonautonomous systems, aperiodically time-dependent vector �elds, transport barriers
Faculty: E.T.S.I. Navales (UPM)
Department: Enseñanzas Básicas de la Ingeniería Naval [hasta 2014]
Creative Commons Licenses: Recognition - No derivative works - Non commercial

Full text

[img]
Preview
PDF - Requires a PDF viewer, such as GSview, Xpdf or Adobe Acrobat Reader
Download (1MB) | Preview

Abstract

In this paper we develop new techniques for revealing geometrical structures in phase space that are valid for aperiodically time dependent dynamical systems, which we refer to as Lagrangian descriptors. These quantities are based on the integration, for a finite time, along trajectories of an intrinsic bounded, positive geometrical and/or physical property of the trajectory itself. We discuss a general methodology for constructing Lagrangian descriptors, and we discuss a “heuristic argument” that explains why this method is successful for revealing geometrical structures in the phase space of a dynamical system. We support this argument by explicit calculations on a benchmark problem having a hyperbolic fixed point with stable and unstable manifolds that are known analytically. Several other benchmark examples are considered that allow us the assess the performance of Lagrangian descriptors in revealing invariant tori and regions of shear. Throughout the paper “side-by-side” comparisons of the performance of Lagrangian descriptors with both finite time Lyapunov exponents (FTLEs) and finite time averages of certain components of the vector field (“time averages”) are carried out and discussed. In all cases Lagrangian descriptors are shown to be both more accurate and computationally efficient than these methods. We also perform computations for an explicitly three dimensional, aperiodically time-dependent vector field and an aperiodically time dependent vector field defined as a data set. Comparisons with FTLEs and time averages for these examples are also carried out, with similar conclusions as for the benchmark examples.

More information

Item ID: 22368
DC Identifier: http://oa.upm.es/22368/
OAI Identifier: oai:oa.upm.es:22368
DOI: 10.1016/j.cnsns.2013.05.002
Official URL: http://www.sciencedirect.com/science/article/pii/S1007570413002037#
Deposited by: Memoria Investigacion
Deposited on: 05 Apr 2014 08:01
Last Modified: 21 Apr 2016 14:16
  • Logo InvestigaM (UPM)
  • Logo GEOUP4
  • Logo Open Access
  • Open Access
  • Logo Sherpa/Romeo
    Check whether the anglo-saxon journal in which you have published an article allows you to also publish it under open access.
  • Logo Dulcinea
    Check whether the spanish journal in which you have published an article allows you to also publish it under open access.
  • Logo de Recolecta
  • Logo del Observatorio I+D+i UPM
  • Logo de OpenCourseWare UPM