About the Jacobi Stability of a Generalized Hopf-Langford System through the Kosambi-Cartan-Chern Geometric Theory

被引：5

作者：

Munteanu, Florian ^{[1
]}

Grin, Alexander ^{[2
]}

Musafirov, Eduard ^{[2
]}

Pranevich, Andrei ^{[2
]}

Sterbeti, Catalin ^{[1
]}

机构：

[1] Univ Craiova, Fac Sci, Dept Appl Math, AI Cuza 13, Craiova 200585, Romania

[2] Yanka Kupala State Univ Grodno, Dept Math Anal, Ozheshko 22, Grodno 230023, BELARUS

来源：

SYMMETRY-BASEL | 2023年 / 15卷 / 03期

关键词：

Hopf-Langford type system; KCC geometric theory; Jacobi stability; the deviation curvature tensor; KCC THEORY;

D O I：

10.3390/sym15030598

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

In this work, we will consider an autonomous three-dimensional quadratic system of first-order ordinary differential equations, with five parameters and with symmetry relative to the z-axis, which generalize the Hopf-Langford system. By reformulating the system as a system of two second-order ordinary differential equations and using the Kosambi-Cartan-Chern (KCC) geometric theory, we will investigate this system from the perspective of Jacobi stability. We will compute the five invariants of KCC theory which determine the own geometrical properties of this system, especially the deviation curvature tensor. Additionally, we will search for necessary and sufficient conditions on the five parameters of the system in order to reach the Jacobi stability around each equilibrium point.

引用

页数：13