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Periodic Solutions and Stability Analysis for Two-Coupled-Oscillator Structure in Optics of Chiral Molecules

Author

Listed:
  • Jing Li

    (Interdisciplinary Research Institute, Faculty of Science, Beijing University of Technology, Beijing 100124, China)

  • Yuying Chen

    (Interdisciplinary Research Institute, Faculty of Science, Beijing University of Technology, Beijing 100124, China)

  • Shaotao Zhu

    (Interdisciplinary Research Institute, Faculty of Science, Beijing University of Technology, Beijing 100124, China
    Faculty of Information Technology, Beijing University of Technology, Beijing 100124, China)

Abstract

Chirality is an indispensable geometric property in the world that has become invariably interlocked with life. The main goal of this paper is to study the nonlinear dynamic behavior and periodic vibration characteristic of a two-coupled-oscillator model in the optics of chiral molecules. We systematically discuss the stability and local dynamic behavior of the system with two pairs of identical conjugate complex eigenvalues. In particular, the existence and number of periodic solutions are investigated by establishing the curvilinear coordinate and constructing a Poincaré map to improve the Melnikov function. Then, we verify the accuracy of the theoretical analysis by numerical simulations, and take a comprehensive look at the nonlinear response of multiple periodic motion under certain conditions. The results might be of important significance for the vibration control, safety stability and design optimization for chiral molecules.

Suggested Citation

  • Jing Li & Yuying Chen & Shaotao Zhu, 2022. "Periodic Solutions and Stability Analysis for Two-Coupled-Oscillator Structure in Optics of Chiral Molecules," Mathematics, MDPI, vol. 10(11), pages 1-24, June.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:11:p:1908-:d:830569
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    References listed on IDEAS

    as
    1. Yoshihisa Inoue, 2005. "Light on chirality," Nature, Nature, vol. 436(7054), pages 1099-1100, August.
    2. Fidele Hategekimana & Snehanshu Saha & Anita Chaturvedi, 2017. "Dynamics of Amoebiasis Transmission: Stability and Sensitivity Analysis," Mathematics, MDPI, vol. 5(4), pages 1-23, November.
    3. Jianming Zhang & Lijun Zhang & Yuzhen Bai, 2019. "Stability and Bifurcation Analysis on a Predator–Prey System with the Weak Allee Effect," Mathematics, MDPI, vol. 7(5), pages 1-15, May.
    4. Seifedine Kadry & Gennady Alferov & Gennady Ivanov & Vladimir Korolev & Ekaterina Selitskaya, 2019. "A New Method to Study the Periodic Solutions of the Ordinary Differential Equations Using Functional Analysis," Mathematics, MDPI, vol. 7(8), pages 1-15, July.
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    Cited by:

    1. Leonid Berlin & Andrey Galyaev & Pavel Lysenko, 2022. "Time-Optimal Control Problem of Two Non-Synchronous Oscillators," Mathematics, MDPI, vol. 10(19), pages 1-19, September.

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