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Memorias de investigación
Research Publications in journals:
A method for revealing phase space structures of general time dependent dynamical systems
Year:2012
Research Areas
  • Mathematics,
  • Physics & space science
Information
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 ?nite time, along tra jectories of an intrinsic bounded, positive geometrical and/or physical property of the tra jectory 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 ?xed 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 ?nite time Lyapunov exponents (FTLEs) and ?nite time averages of certain components of the vector ?eld (?time averages?) are carried out and discussed. In all cases Lagrangian descriptors are shown to be both more accurate and computationally e?cient than these methods. We also perform computations for an explicitly three dimensional, aperiodically time-dependent vector ?eld and an aperiodically time dependent vector ?eld de?ned 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.
International
Si
JCR
Si
Title
Communications in Nonlinear Science And Numerical Simulation
ISBN
1007-5704
Impact factor JCR
2,806
Impact info
Volume
18
Journal number
12
From page
3530
To page
3557
Month
SIN MES
Ranking
Participants
  • Autor: Ana María Mancho (CSIC)
  • Autor: Stephen Wiggins (University of Bristol)
  • Autor: Jezabel Curbelo (Universidad Autónoma de Madrid)
  • Autor: Carolina Andrea Mendoza Parra (UPM)
Research Group, Departaments and Institutes related
  • Creador: Departamento: Ciencias Aplicadas a la Ingeniería Naval
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