New Insights on Non-integrability and Dynamics in a Simple Quadratic Differential System

IF 1.4 4区 物理与天体物理 Q2 MATHEMATICS, APPLIED
Jingjia Qu, Shuangling Yang
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引用次数: 0

Abstract

This study focuses on the integrability and qualitative behaviors of a quadratic differential system

$$\dot{x}=a+yz,\quad\dot{y}=-y + x^{2},\quad\dot{z}=b-4x.$$

We provide some new perspectives on the system and reveal its diverse properties, including non-integrability in the sense of absence of first integrals, bifurcations of co-dimension one or two, Jacobi instability and dynamics at infinity.

Abstract Image

简单二次微分系统的不可控性和动力学新见解
本研究重点关注二次微分系统 $$\dot{x}=a+yz,\quad\dot{y}=-y + x^{2},\quad\dot{z}=b-4x 的可整性和定性行为。我们为该系统提供了一些新的视角,并揭示了它的多种特性,包括无初积分意义上的非可整性、一维或二维分岔、雅可比不稳定性和无穷大时的动力学。
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来源期刊
Journal of Nonlinear Mathematical Physics
Journal of Nonlinear Mathematical Physics PHYSICS, MATHEMATICAL-PHYSICS, MATHEMATICAL
CiteScore
1.60
自引率
0.00%
发文量
67
审稿时长
3 months
期刊介绍: Journal of Nonlinear Mathematical Physics (JNMP) publishes research papers on fundamental mathematical and computational methods in mathematical physics in the form of Letters, Articles, and Review Articles. Journal of Nonlinear Mathematical Physics is a mathematical journal devoted to the publication of research papers concerned with the description, solution, and applications of nonlinear problems in physics and mathematics. The main subjects are: -Nonlinear Equations of Mathematical Physics- Quantum Algebras and Integrability- Discrete Integrable Systems and Discrete Geometry- Applications of Lie Group Theory and Lie Algebras- Non-Commutative Geometry- Super Geometry and Super Integrable System- Integrability and Nonintegrability, Painleve Analysis- Inverse Scattering Method- Geometry of Soliton Equations and Applications of Twistor Theory- Classical and Quantum Many Body Problems- Deformation and Geometric Quantization- Instanton, Monopoles and Gauge Theory- Differential Geometry and Mathematical Physics
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