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

J. J. Barba-Franco | Zendy; P.B. Espinoza | Zendy; A. Gallegos | Zendy; R. Jaimes-Reátegui | Zendy; Jorge E. MacíasDíaz | Zendy

Open Access

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

Author(s) -

J. J. Barba-Franco,

P.B. Espinoza,

A. Gallegos,

R. Jaimes-Reátegui,

Jorge E. MacíasDíaz

Publication year - 2020

Publication title -

revista mexicana de física

Language(s) - English

Resource type - Journals

eISSN - 2683-2224

pISSN - 0035-001X

DOI - 10.31349/revmexfis.66.440

Subject(s) - dissipative system , logarithm , physics , duffing equation , coupling parameter , coupling (piping) , statistical physics , bifurcation , classical mechanics , mathematical analysis , mathematics , quantum mechanics , nonlinear system , mechanical engineering , engineering

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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