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Validating the physical model of a chaotic system by topological analysis

Javier Used1,* and Juan Carlos Martín2,†

  • 1Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Física Universidad Rey Juan Carlos, Tulipán s/n, 28933 Móstoles, Madrid, Spain
  • 2Departamento de Física Aplicada, Universidad de Zaragoza, Pedro Cerbuna 12, 50009 Zaragoza, Spain

  • *javier.used@urjc.es
  • †jcmartin@unizar.es
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Phys. Rev. E 87, 052921 – Published 31 May, 2013

DOI: https://doi.org/10.1103/PhysRevE.87.052921

Abstract

Topological analysis is employed for the first time to our knowledge as a method of validation for a physical model describing a chaotic system. Topological analysis theory provides both a way to characterize the topological structure of chaotic attractors by means of a set of integer numbers and a method to obtain this set departing from a time series generated by the chaotic system. The validation method proposed here consists of comparing the topological structure of chaotic attractors obtained from time series generated on the one hand by an experimental system and on the other hand by the numerical model under test. This procedure has been applied to an erbium-doped fiber laser subject to pump power sine-wave modulation.

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Phys. Rev. E 87, 052921– Published 31 May, 2013
  • Received 25 February 2013

©2013 American Physical Society

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