On the Lagrangians and potentials of a two coupled damped Duffing oscillators system and their application on three-node motif networks

Authors

  • J. J. Barba-Franco, Departamento de Ciencias Exactas y Tecnologia, Centro Universitario de los Lagos, Universidad de Guadalajara, Avenida Enrique Diaz de Leon No. 1144, Colonia Paseos de la Montaña, Lagos de Moreno, Jal. 47460, Mexico. http://orcid.org/0000-0002-2866-4306
  • P. B. Espinoza, Departamento de Ciencias Exactas y Tecnologia, Centro Universitario de los Lagos, Universidad de Guadalajara, Avenida Enrique Diaz de Leon No. 1144, Colonia Paseos de la Montaña, Lagos de Moreno, Jal. 47460, Mexico.
  • A. Gallegos, Departamento de Ciencias Exactas y Tecnologia, Centro Universitario de los Lagos, Universidad de Guadalajara, Avenida Enrique Diaz de Leon No. 1144, Colonia Paseos de la Montaña, Lagos de Moreno, Jal. 47460, Mexico.
  • R. Jaimes-Reategui Departamento de Ciencias Exactas y Tecnologia, Centro Universitario de los Lagos, Universidad de Guadalajara, Avenida Enrique Diaz de Leon No. 1144, Colonia Paseos de la Montaña, Lagos de Moreno, Jal. 47460, Mexico.
  • J.E. Macias-Diaz Departamento de Matematicas y Fisica, Universidad Autonoma de Aguascalientes, Avenida Universidad 940, Ciudad Universitaria, Aguascalientes, Ags. 20131, Mexico.

DOI:

https://doi.org/10.31349/RevMexFis.66.440

Keywords:

Duffing oscillator, motif network, Lagrangian, coupled oscillators, damped systems

Abstract

In this work, we investigate the Lagrangians and potentials for two coupled damped Duffing oscillators both directionally and bi-directionally. We show that, although it is not always possible to define a potential in dissipative systems, the potential of our model can be defined if the damping coefficient has a logarithmic derivative form. It is possible to apply these results to the analysis of the dynamics of complex networks based on three-node motif configurations. As an example, we study numerically the dynamics for one of the thirteen different possible configurations. Here, the phenomenon of synchronization is observed in terms of the coupling parameter.

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Published

2020-07-01

How to Cite

[1]
J. J. Barba-Franco, P. B. Espinoza, A. Gallegos, R. Jaimes-Reategui, and J. Macias-Diaz, “On the Lagrangians and potentials of a two coupled damped Duffing oscillators system and their application on three-node motif networks”, Rev. Mex. Fís., vol. 66, no. 4 Jul-Aug, pp. 440–445, Jul. 2020.

Issue

Vol. 66 No. 4 Jul-Aug (2020): Revista Mexicana de Física

Section

07 Gravitation, Mathematical Physics and Field Theory

License

Authors retain copyright and grant the Revista Mexicana de Física right of first publication with the work simultaneously licensed under a CC BY-NC-ND 4.0 that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.