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2-D Duffing Oscillator: Elliptic Functions from a Dynamical Systems Point of View

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An Erratum to this article was published on 06 March 2013

Abstract

K. Meyer has advocated for the study of elliptic functions and integrals from a dynamical systems point of view. Here, we follow his advice and we propose the bidimensional Hamiltonian Duffing oscillator as a model; it allows us to deal with the elliptic integral of third kind directly. Focusing on bounded trajectories we do a detailed analysis of the solutions in the three regions defined by the parameters. In our opinion, for the study of elliptic functions, the model presented here represents an alternative to the pendulum or the free rigid body systems.

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Authors and Affiliations

  1. Departamento de Matemática Aplicada, Universidad de Murcia, Campus de Espinardo, 30071, Espinardo, Murcia, Spain

    Francisco Javier Molero, Martín Lara, Sebastián Ferrer & Francisco Céspedes

Authors
  1. Francisco Javier Molero
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  2. Martín Lara
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  3. Sebastián Ferrer
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  4. Francisco Céspedes
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Correspondence to Francisco Javier Molero.

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In Honor of Ken R. Meyer.

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Molero, F.J., Lara, M., Ferrer, S. et al. 2-D Duffing Oscillator: Elliptic Functions from a Dynamical Systems Point of View. Qual. Theory Dyn. Syst. 12, 115–139 (2013). https://doi.org/10.1007/s12346-012-0081-1

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