On the local energy conservation of a system of three unidirectionally coupled undamped forced Duffing oscillators and their dynamics
DOI:
https://doi.org/10.31349/RevMexFis.71.060702Keywords:
lagrangian, conserved quantities, coupled oscillators, undamped systems, phase space analysisAbstract
The Duffing oscillator is a well-established model with broad applications in physics, engineering, and biological systems. This study examines a system of three undamped, non-autonomous Duffing oscillators arranged in a unidirectionally coupled ring configuration. The model enables the exploration of intricate dynamical behaviors, including multistability, synchronization, and the onset of chaos. Local energy conservation is analyzed through integrals of motion and phase-space examination, considering various coupling strengths and natural frequency parameters. By applying the Milne-Pinney equations, the study identifies three conserved quantities—each associated with an oscillator—whose interdependence reflects the structural influence of the ring. The findings demonstrate how unidirectional coupling and non-autonomous forcing facilitate energy exchanges within the system, revealing that local energy conservation is not merely a consequence of global symmetries but rather emerges from the complex interplay of nonlinear interactions. This deeper perspective enhances the understanding of energy dynamics in coupled oscillatory systems.
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Copyright (c) 2025 I.A. Alvarado-López , F.J. Carmona-Moreno, E. Urenda-Cázares, J.J. Barba-Franco
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