Stability Analysis of a Differential Model for Quasi-Periodic Plasma Perturbations

Le Deng; Bo Huang; Wei Niu; Jichao Song; Xinyu Wang

doi:10.1007/978-3-031-69070-9_8

Stability Analysis of a Differential Model for Quasi-Periodic Plasma Perturbations

Le Deng
, Bo Huang^*
, Wei Niu
, Jichao Song
, Xinyu Wang

^*Corresponding author for this work

Beihang University
Beihang Hangzhou Innovation Institute Yuhang

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

This paper deals with the stability of a differential model for quasi-periodic plasma perturbations. First, we derive the linear stability conditions on the parameters of the differential model by using symbolic computation of solving semi-algebraic systems. Then, we analyze the Jacobi stability of the quasi-periodic plasma perturbations by using the Kosambi–Cartan–Chern (KCC) theory. We reformulate the differential model as a set of two second-order nonlinear differential equations and explicitly obtain the geometric invariants, as well as the deviation curvature tensor. The Jacobi stability of the fixed points of the system is detected by using computer algebra methods. Furthermore, the dynamic behavior of the components of the deviation vector near the fixed points is also discussed. The obtained results show that all the fixed points of the differential model are always Jacobi unstable, while the linear stability of the fixed points depends on the values of the parameters. Some examples and numerical simulations are presented to verify the established results.

Original language	English
Title of host publication	Computer Algebra in Scientific Computing - 26th International Workshop, CASC 2024, Proceedings
Editors	François Boulier, Chenqi Mou, Timur M. Sadykov, Evgenii V. Vorozhtsov
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	120-139
Number of pages	20
ISBN (Print)	9783031690693
DOIs	https://doi.org/10.1007/978-3-031-69070-9_8
State	Published - 2024
Event	26th International Workshop on Computer Algebra in Scientific Computing, CASC 2024 - Rennes, France Duration: 2 Sep 2024 → 6 Sep 2024

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	14938 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	26th International Workshop on Computer Algebra in Scientific Computing, CASC 2024
Country/Territory	France
City	Rennes
Period	2/09/24 → 6/09/24

Keywords

Differential model
Jacobi stability
KCC theory
Linear stability
Symbolic computation

Access to Document

10.1007/978-3-031-69070-9_8

Cite this

Deng, L., Huang, B., Niu, W., Song, J., & Wang, X. (2024). Stability Analysis of a Differential Model for Quasi-Periodic Plasma Perturbations. In F. Boulier, C. Mou, T. M. Sadykov, & E. V. Vorozhtsov (Eds.), Computer Algebra in Scientific Computing - 26th International Workshop, CASC 2024, Proceedings (pp. 120-139). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 14938 LNCS). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-031-69070-9_8

Deng, Le ; Huang, Bo ; Niu, Wei et al. / Stability Analysis of a Differential Model for Quasi-Periodic Plasma Perturbations. Computer Algebra in Scientific Computing - 26th International Workshop, CASC 2024, Proceedings. editor / François Boulier ; Chenqi Mou ; Timur M. Sadykov ; Evgenii V. Vorozhtsov. Springer Science and Business Media Deutschland GmbH, 2024. pp. 120-139 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "This paper deals with the stability of a differential model for quasi-periodic plasma perturbations. First, we derive the linear stability conditions on the parameters of the differential model by using symbolic computation of solving semi-algebraic systems. Then, we analyze the Jacobi stability of the quasi-periodic plasma perturbations by using the Kosambi–Cartan–Chern (KCC) theory. We reformulate the differential model as a set of two second-order nonlinear differential equations and explicitly obtain the geometric invariants, as well as the deviation curvature tensor. The Jacobi stability of the fixed points of the system is detected by using computer algebra methods. Furthermore, the dynamic behavior of the components of the deviation vector near the fixed points is also discussed. The obtained results show that all the fixed points of the differential model are always Jacobi unstable, while the linear stability of the fixed points depends on the values of the parameters. Some examples and numerical simulations are presented to verify the established results.",

keywords = "Differential model, Jacobi stability, KCC theory, Linear stability, Symbolic computation",

author = "Le Deng and Bo Huang and Wei Niu and Jichao Song and Xinyu Wang",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.; 26th International Workshop on Computer Algebra in Scientific Computing, CASC 2024 ; Conference date: 02-09-2024 Through 06-09-2024",

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doi = "10.1007/978-3-031-69070-9\_8",

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Deng, L, Huang, B , Niu, W, Song, J & Wang, X 2024, Stability Analysis of a Differential Model for Quasi-Periodic Plasma Perturbations. in F Boulier, C Mou, TM Sadykov & EV Vorozhtsov (eds), Computer Algebra in Scientific Computing - 26th International Workshop, CASC 2024, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 14938 LNCS, Springer Science and Business Media Deutschland GmbH, pp. 120-139, 26th International Workshop on Computer Algebra in Scientific Computing, CASC 2024, Rennes, France, 2/09/24. https://doi.org/10.1007/978-3-031-69070-9_8

Stability Analysis of a Differential Model for Quasi-Periodic Plasma Perturbations. / Deng, Le; Huang, Bo ; Niu, Wei et al.
Computer Algebra in Scientific Computing - 26th International Workshop, CASC 2024, Proceedings. ed. / François Boulier; Chenqi Mou; Timur M. Sadykov; Evgenii V. Vorozhtsov. Springer Science and Business Media Deutschland GmbH, 2024. p. 120-139 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 14938 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Deng, Le

AU - Huang, Bo

AU - Niu, Wei

AU - Song, Jichao

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N1 - Publisher Copyright: © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.

PY - 2024

Y1 - 2024

N2 - This paper deals with the stability of a differential model for quasi-periodic plasma perturbations. First, we derive the linear stability conditions on the parameters of the differential model by using symbolic computation of solving semi-algebraic systems. Then, we analyze the Jacobi stability of the quasi-periodic plasma perturbations by using the Kosambi–Cartan–Chern (KCC) theory. We reformulate the differential model as a set of two second-order nonlinear differential equations and explicitly obtain the geometric invariants, as well as the deviation curvature tensor. The Jacobi stability of the fixed points of the system is detected by using computer algebra methods. Furthermore, the dynamic behavior of the components of the deviation vector near the fixed points is also discussed. The obtained results show that all the fixed points of the differential model are always Jacobi unstable, while the linear stability of the fixed points depends on the values of the parameters. Some examples and numerical simulations are presented to verify the established results.

AB - This paper deals with the stability of a differential model for quasi-periodic plasma perturbations. First, we derive the linear stability conditions on the parameters of the differential model by using symbolic computation of solving semi-algebraic systems. Then, we analyze the Jacobi stability of the quasi-periodic plasma perturbations by using the Kosambi–Cartan–Chern (KCC) theory. We reformulate the differential model as a set of two second-order nonlinear differential equations and explicitly obtain the geometric invariants, as well as the deviation curvature tensor. The Jacobi stability of the fixed points of the system is detected by using computer algebra methods. Furthermore, the dynamic behavior of the components of the deviation vector near the fixed points is also discussed. The obtained results show that all the fixed points of the differential model are always Jacobi unstable, while the linear stability of the fixed points depends on the values of the parameters. Some examples and numerical simulations are presented to verify the established results.

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KW - Jacobi stability

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KW - Linear stability

KW - Symbolic computation

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Deng L, Huang B , Niu W, Song J, Wang X. Stability Analysis of a Differential Model for Quasi-Periodic Plasma Perturbations. In Boulier F, Mou C, Sadykov TM, Vorozhtsov EV, editors, Computer Algebra in Scientific Computing - 26th International Workshop, CASC 2024, Proceedings. Springer Science and Business Media Deutschland GmbH. 2024. p. 120-139. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-031-69070-9_8