Jacobi Stability for T-System

In this paper will be considered a three-dimensional autonomous quadratic polynomial system of first-order differential equations with three real parameters, the so-called T-system. This system is symmetric relative to the <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Florian Munteanu [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2024

Schlagwörter:	T-system the deviation curvature tensor Jacobi stability KCC geometric theory

Übergeordnetes Werk:	In: Symmetry - MDPI AG, 2009, 16(2024), 1, p 84
Übergeordnetes Werk:	volume:16 ; year:2024 ; number:1, p 84

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.3390/sym16010084

Katalog-ID:	DOAJ096299126

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language	English
source	In Symmetry 16(2024), 1, p 84 volume:16 year:2024 number:1, p 84
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author	Florian Munteanu
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topic_title	QA1-939 Jacobi Stability for T-System T-system the deviation curvature tensor Jacobi stability KCC geometric theory
topic	misc QA1-939 misc T-system misc the deviation curvature tensor misc Jacobi stability misc KCC geometric theory misc Mathematics
topic_unstemmed	misc QA1-939 misc T-system misc the deviation curvature tensor misc Jacobi stability misc KCC geometric theory misc Mathematics
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title	Jacobi Stability for T-System
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abstract	In this paper will be considered a three-dimensional autonomous quadratic polynomial system of first-order differential equations with three real parameters, the so-called T-system. This system is symmetric relative to the <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<O</mi<<mi<z</mi<</mrow<</semantics<</math<</inline-formula<-axis and represents a special type of the generalized Lorenz system. The approach of this work will consist of the study of the nonlinear dynamics of this system through the Kosambi–Cartan–Chern (KCC) geometric theory. More exactly, we will focus on the associated system of second-order differential equations (SODE) from the point of view of Jacobi stability by determining the five invariants of the KCC theory. These invariants determine the internal geometrical characteristics of the system, and particularly, the deviation curvature tensor is decisive for Jacobi stability. Furthermore, we will look for necessary and sufficient conditions that the system parameters must satisfy in order to have Jacobi stability for every equilibrium point.
abstractGer	In this paper will be considered a three-dimensional autonomous quadratic polynomial system of first-order differential equations with three real parameters, the so-called T-system. This system is symmetric relative to the <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<O</mi<<mi<z</mi<</mrow<</semantics<</math<</inline-formula<-axis and represents a special type of the generalized Lorenz system. The approach of this work will consist of the study of the nonlinear dynamics of this system through the Kosambi–Cartan–Chern (KCC) geometric theory. More exactly, we will focus on the associated system of second-order differential equations (SODE) from the point of view of Jacobi stability by determining the five invariants of the KCC theory. These invariants determine the internal geometrical characteristics of the system, and particularly, the deviation curvature tensor is decisive for Jacobi stability. Furthermore, we will look for necessary and sufficient conditions that the system parameters must satisfy in order to have Jacobi stability for every equilibrium point.
abstract_unstemmed	In this paper will be considered a three-dimensional autonomous quadratic polynomial system of first-order differential equations with three real parameters, the so-called T-system. This system is symmetric relative to the <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<O</mi<<mi<z</mi<</mrow<</semantics<</math<</inline-formula<-axis and represents a special type of the generalized Lorenz system. The approach of this work will consist of the study of the nonlinear dynamics of this system through the Kosambi–Cartan–Chern (KCC) geometric theory. More exactly, we will focus on the associated system of second-order differential equations (SODE) from the point of view of Jacobi stability by determining the five invariants of the KCC theory. These invariants determine the internal geometrical characteristics of the system, and particularly, the deviation curvature tensor is decisive for Jacobi stability. Furthermore, we will look for necessary and sufficient conditions that the system parameters must satisfy in order to have Jacobi stability for every equilibrium point.
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