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Volume 4, Issue 3
The First Integrals and Related Properties of a Class of Quintic Systems with a Uniform Isochronous Center

Yuexin Yan & Zhengxin Zhou

DOI: 10.12150/jnma.2022.488

J. Nonl. Mod. Anal., 4 (2022), pp. 488-501.

Published online: 2022-06

[An open-access article; the PDF is free to any online user.]

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  • Abstract

In this paper, we give all the first integrals of the quintic systems which have a uniform isochronous center, and use them to determine the qualitative behavior of the periodic solutions of their equivalent non-autonomous systems. Meanwhile, we clearly describe the local phase portraits of singularity at infinity.

  • Keywords

First integrals, Equivalence system, Uniform isochronous center, Infinite singularity, Local phase portraits.

  • AMS Subject Headings

34C07, 34C05, 34C25, 37G15

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JNMA-4-488, author = {Yan , Yuexin and Zhou , Zhengxin}, title = {The First Integrals and Related Properties of a Class of Quintic Systems with a Uniform Isochronous Center}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2022}, volume = {4}, number = {3}, pages = {488--501}, abstract = {

In this paper, we give all the first integrals of the quintic systems which have a uniform isochronous center, and use them to determine the qualitative behavior of the periodic solutions of their equivalent non-autonomous systems. Meanwhile, we clearly describe the local phase portraits of singularity at infinity.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2022.488}, url = {http://global-sci.org/intro/article_detail/jnma/20720.html} }
TY - JOUR T1 - The First Integrals and Related Properties of a Class of Quintic Systems with a Uniform Isochronous Center AU - Yan , Yuexin AU - Zhou , Zhengxin JO - Journal of Nonlinear Modeling and Analysis VL - 3 SP - 488 EP - 501 PY - 2022 DA - 2022/06 SN - 4 DO - http://doi.org/10.12150/jnma.2022.488 UR - https://global-sci.org/intro/article_detail/jnma/20720.html KW - First integrals, Equivalence system, Uniform isochronous center, Infinite singularity, Local phase portraits. AB -

In this paper, we give all the first integrals of the quintic systems which have a uniform isochronous center, and use them to determine the qualitative behavior of the periodic solutions of their equivalent non-autonomous systems. Meanwhile, we clearly describe the local phase portraits of singularity at infinity.

Yuexin Yan & Zhengxin Zhou. (2022). The First Integrals and Related Properties of a Class of Quintic Systems with a Uniform Isochronous Center. Journal of Nonlinear Modeling and Analysis. 4 (3). 488-501. doi:10.12150/jnma.2022.488
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