Abstract

BARBA-FRANCO, J. J. et al. On the Lagrangians and potentials of a two coupled damped Duffing oscillators system and their application on three-node motif networks. Rev. mex. fis. [online]. 2020, vol.66, n.4, pp.440-445.  Epub Jan 31, 2022. ISSN 0035-001X.  https://doi.org/10.31349/revmexfis.66.440.

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.

Keywords : Duffing oscillator; motif network; Lagrangian; coupled oscillators; damped systems.

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