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

Mancho, Ana María; Wiggins, Stephen; Curbelo, Jezabel y 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.

Descripción

Título: A method for revealing phase space structures of general time dependent dynamical systems
Autor/es:
  • Mancho, Ana María
  • Wiggins, Stephen
  • Curbelo, Jezabel
  • Mendoza Parra, Carolina Andrea
Tipo de Documento: Artículo
Título de Revista/Publicación: Communications in Nonlinear Science and Numerical Simulation
Fecha: Noviembre 2013
Volumen: 18
Materias:
Palabras Clave Informales: Invariant manifolds, nonautonomous systems, aperiodically time-dependent vector �elds, transport barriers
Escuela: E.T.S.I. Navales (UPM)
Departamento: Enseñanzas Básicas de la Ingeniería Naval [hasta 2014]
Licencias Creative Commons: Reconocimiento - Sin obra derivada - No comercial

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Resumen

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.

Más información

ID de Registro: 22368
Identificador DC: http://oa.upm.es/22368/
Identificador OAI: oai:oa.upm.es:22368
Identificador DOI: 10.1016/j.cnsns.2013.05.002
URL Oficial: http://www.sciencedirect.com/science/article/pii/S1007570413002037#
Depositado por: Memoria Investigacion
Depositado el: 05 Abr 2014 08:01
Ultima Modificación: 21 Abr 2016 14:16
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