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

College of Applied Sciences, Beijing University of Technology, Beijing 100124, China
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Mathematics 2019, 7(12), 1218; https://doi.org/10.3390/math7121218
Received: 6 November 2019 / Revised: 4 December 2019 / Accepted: 6 December 2019 / Published: 10 December 2019
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. View Full-Text
Keywords: four-dimensional coupled system; periodic solutions; existence condition; parameter control conditions; circular mesh antenna model four-dimensional coupled system; periodic solutions; existence condition; parameter control conditions; circular mesh antenna model
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Tian, Y.; Li, J. Periodic Solutions for a Four-Dimensional Coupled Polynomial System with N-Degree Homogeneous Nonlinearities. Mathematics 2019, 7, 1218.

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