An integral of motion for a Master–Slave system of damped Duffing oscillators with variable coefficients: Nonlinear dynamics and computer simulations

José de Jesús Barba-Franco (), Armando Gallegos (), Ernesto Urenda-Cázares and Jorge E. Macías-Díaz
Additional contact information
José de Jesús Barba-Franco: Departamento de Ciencias Básicas, Instituto Tecnológico Nacional de México, Instituto Tecnológico José Mario Molina Pasquel y Henríquez, Calle José Guadalupe Tejeda Vázquez, Arandas, 47180 Jalisco, Mexico
Armando Gallegos: Departamento de Ciencias Exactas y Tecnología, Centro Universitario de los Lagos, Universidad de Guadalajara, Enrique Díaz de León 1144, Lagos de Moreno, 10587 Jalisco, Mexico
Ernesto Urenda-Cázares: Departamento de Matemáticas, Centro Universitario de Ciencias Exactas e Ingenierías, Universidad de Guadalajara, Boulevard General Marcelino García Barragán 1421, Guadalajara, 44430 Jalisco, Mexico4Departamento de Ingenierías, Centro Universitario de los Altos, Universidad de Guadalajara, Avenida Rafael Casillas Aceves 1200, Tepatitlán de Morelos, 47620 Jalisco, Mexico
Jorge E. Macías-Díaz: Department of Mathematics and Didactics of Mathematics, School of Digital Technologies, Tallinn University, Narva Rd. 25, Tallinn, 10120 Harju, Estonia6Departamento de Matemáticas y Física, Universidad Autónoma de Aguascalientes, Avenida Universidad 940, Ciudad Universitaria, Aguascalientes, 20100 Aguascalientes, Mexico

International Journal of Modern Physics C (IJMPC), 2024, vol. 35, issue 12, 1-19

Abstract: In this work, a master–slave system composed by a pair of damped Duffing oscillators with variable coefficients and nonlinear coupling is investigated. An integral of motion for the system is obtained using a symmetry transformation and Noether’s theorem. Some numerical examples are presented for different cases of damping and oscillation frequency, for a varying coupling constant. The system dynamics is studied by means of space-time surfaces, time series and phase portraits. For a constant oscillation frequency, the slave presents envelopes that tend to become chaotic as the coupling constant increases. Meanwhile, as the frequency increases with time, the slave has higher amplitudes and speeds than the master oscillator.

Keywords: Parametric-coupled damped oscillators; symmetry transformation; Noether’s theorem; master–slave coupling; integral of motion (search for similar items in EconPapers)
Date: 2024
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S012918312450150X
Access to full text is restricted to subscribers

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:ijmpcx:v:35:y:2024:i:12:n:s012918312450150x

Ordering information: This journal article can be ordered from

DOI: 10.1142/S012918312450150X

Access Statistics for this article

International Journal of Modern Physics C (IJMPC) is currently edited by H. J. Herrmann

More articles in International Journal of Modern Physics C (IJMPC) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().