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

Author

Listed:
  • 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)

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.

Suggested Citation

  • José de Jesús Barba-Franco & Armando Gallegos & Ernesto Urenda-Cázares & Jorge E. Macías-Díaz, 2024. "An integral of motion for a Master–Slave system of damped Duffing oscillators with variable coefficients: Nonlinear dynamics and computer simulations," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 35(12), pages 1-19, December.
    • Handle: RePEc:wsi:ijmpcx:v:35:y:2024:i:12:n:s012918312450150x
    DOI: 10.1142/S012918312450150X
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