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Periodic Solutions for a Four-Dimensional Coupled Polynomial System with N-Degree Homogeneous Nonlinearities
- Source :
- Mathematics, Volume 7, Issue 12
- Publication Year :
- 2019
- Publisher :
- Multidisciplinary Digital Publishing Institute, 2019.
-
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.
- Subjects :
- Polynomial
circular mesh antenna model
Degree (graph theory)
Generalization
General Mathematics
010102 general mathematics
Mathematical analysis
Linear system
Trigonometric integral
four-dimensional coupled system
periodic solutions
Expression (computer science)
Singular point of a curve
01 natural sciences
Resonance (particle physics)
0103 physical sciences
Computer Science (miscellaneous)
parameter control conditions
0101 mathematics
010301 acoustics
Engineering (miscellaneous)
Mathematics
existence condition
Subjects
Details
- Language :
- English
- ISSN :
- 22277390
- Database :
- OpenAIRE
- Journal :
- Mathematics
- Accession number :
- edsair.doi.dedup.....5fceca97eed1d5d4527fb7d36c1bfb39
- Full Text :
- https://doi.org/10.3390/math7121218