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Title: Integral of motion and nonlinear dynamics of three Duffing oscillators with weak or strong bidirectional coupling
Authors: Urenda Cázares, Ernesto
Barba Franco, José de Jesús
Gallegos, Armando
Macías Díaz, Jorge E.
Keywords: bidirectional coupling
coupled three Duffing oscillators
integrals of motion
chaotic networks
nonlinear dynamics
Issue Date: Oct-2023
Publisher: Springer Nature
Citation: Urenda-Cázares, E., de Jesús Barba-Franco, J., Gallegos, A. et al. Integral of motion and nonlinear dynamics of three Duffing oscillators with weak or strong bidirectional coupling. Nonlinear Dyn 111, 18953–18968 (2023).
Series/Report no.: Nonlinear Dynamics;111, (20), 18953–18968 (2023)
Abstract: In this work, we present a system composed of three identical Duffing oscillators coupled bidirectionally. Starting from a Lagrangian that describes the system, an integral of motion is obtained by means of Noether’s theorem. The dynamics of the model is studied using bifurcation diagrams, Lyapunov exponents, time-series analysis, phase spaces, Poincaré sections, spatiotemporal and integral of motion planes. The analysis focuses on the monostable and bistable cases of the Duffing oscillator potential, in which a confined movement is guaranteed. In particular, it is observed that the system shows a chaotic behavior for small values of the coupling parameter for the bistable case. This is one of the first articles in the literature in which non-trivial integrals of motion are obtained for a system of three Duffing oscillators coupled bidirectionally. It is worth pointing out that there are some reports in the literature on integrals of motion for unidirectionally coupled nonlinear Duffing oscillators, but the study carried out in this work for bidirectionally coupled systems with more than two nonlinear Duffing oscillators is certainly one of the first.
Description: Artículo
ISSN: 1573-269X online
0924-090X print
Appears in Collections:1203 Artículos

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