Asymmetric Duffing oscillator: the birth and build-up of a period-doubling cascade

• Autorzy: Kyzioł Jan , Okniński Andrzej

Identyfikatory

DOI

10.15632/jtam-pl/193829

• Języki publikacji: EN

Abstrakty

EN

We investigate the period-doubling phenomenon in aperiodically forced asymmetric Duffing oscillator. We use the known steady-state asymptotic solution – the amplitude-frequency implicit function – and known criterion for the existence of period-doubling, also in an implicit form. Working in the framework of differential properties of implicit functions, we derive analytical formulas for the birth of period-doubled solutions.

Słowa kluczowe

EN

Duffing equation; period-doubling; implicit function

• Wydawca: Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
• Czasopismo: Journal of Theoretical and Applied Mechanics
• Rocznik: 2024
• Tom: Vol. 62 nr 4
• Strony: 713--719
• Opis fizyczny: Bibliogr. 12 poz., rys., tab.

Twórcy

autor

Kyzioł Jan

• Kielce University of Technology, Kielce, Poland

• https://orcid.org/0000-0002-8721-8250

autor

Okniński Andrzej

• Kielce University of Technology, Kielce, Poland

• https://orcid.org/0000-0002-6306-4293

Bibliografia

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• 3. Jordan D.W., Smith P., 1999, Nonlinear Ordinary Differential Equations: An Introduction to Dynamical Systems, Oxford University Press, New York.
• 4. Kovacic I., Brennan M.J., 2011, Forced harmonic vibration of an asymmetric Duffing oscillator, [In:] The Duffing Equation: Nonlinear Oscillators and Their Behavior, I. Kovacic, M.J. Brennan (Edit.), John Wiley & Sons, Hoboken, New Jersey, 277-322.
• 5. Kyzioł J., Okniński A., 2022, Localizing bifurcations in non-linear dynamical systems via analytical and numerical methods, Processes, 10, 1, 127.
• 6. Kyzioł J., Okniński A., 2023, Asymmetric Duffing oscillator: jump manifold and border set, Nonlinear Dynamics and Systems Theory, 23, 1, 46-57.
• 7. Nusse H.E., Yorke J.A., 1998, Dynamics: Numerical Explorations, Accompanying Computer Program Dynamics, Applied Mathematical Sciences, 101, Springer.
• 8. Szemplińska-Stupnicka W., 1987, Secondary resonances and approximate models of routes to chaotic motion in non-linear oscillators, Journal of Sound and Vibration, 113, 1, 155-172.
• 9. Szemplińska-Stupnicka W., 1988, Bifurcations of harmonic solution leading to chaotic motion in the softening type Duffing’s oscillator, International Journal of Non-Linear Mechanics, 23, 4, 257-277.
• 10. Szemplińska-Stupnicka W., Bajkowski J., 1986, The 12 subharmonic resonance and its transition to chaotic motion in a non-linear oscillator, International Journal of Non-Linear Mechanics, 21, 5, 401-419.
• 11. Wolfram Research, Inc., 2020, Mathematica, Version 12.1, Champaign, IL.
• 12. Xu Y., Luo A.C.J., 2020, Independent period-2 motions to chaos in a van der Pol-Duffing oscillator, International Journal of Bifurcation and Chaos, 30, 15, 2030045.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).