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Periodic Solutions for a Four-Dimensional Coupled Polynomial System with N-Degree Homogeneous Nonlinearities

Author

Listed:
  • Yuanyuan Tian

    (College of Applied Sciences, Beijing University of Technology, Beijing 100124, China)

  • Jing Li

    (College of Applied Sciences, Beijing University of Technology, Beijing 100124, China)

Abstract

This paper studies the periodic solutions of a four-dimensional coupled polynomial system with N-degree homogeneous nonlinearities of which the unperturbed linear system has a center singular point in generalization resonance 1 : n at the origin. Considering arbitrary positive integers n and N with n ≤ N and N ≥ 2 , the new explicit expression of displacement function for the four-dimensional system is detected by introducing the technique on power trigonometric integrals. Then some precise and detailed results in comparison with the existing works, including the existence condition, the exact number, and the parameter control conditions of periodic solutions, are obtained, which can provide a new theoretical description and mechanism explanation for the phenomena of emergence and disappearance of periodic solutions. Results obtained in this paper improve certain existing results under some parameter conditions and can be extensively used in engineering applications. To verify the applicability and availability of the new theoretical results, as an application, the periodic solutions of a circular mesh antenna model are obtained by theoretical method and numerical simulations.

Suggested Citation

  • Yuanyuan Tian & Jing Li, 2019. "Periodic Solutions for a Four-Dimensional Coupled Polynomial System with N-Degree Homogeneous Nonlinearities," Mathematics, MDPI, vol. 7(12), pages 1-21, December.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:12:p:1218-:d:296357
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    References listed on IDEAS

    as
    1. Yang, Junmin & Ding, Wei, 2018. "Limit cycles of a class of Liénard systems with restoring forces of seventh degree," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 422-437.
    2. 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.
    Full references (including those not matched with items on IDEAS)

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