曲阜师范大学学报（自然科学版）2025，Vol.51Issue(4)：38-48,11.DOI:10.3969/j.issn.1001-5337.2025.4.038
一类带阻尼SD振子的Jacobi分析
Jacobi analysis of a type of damped SD oscillators
摘要
Abstract
Based on Kosambi-Cartan-Chern(KCC)theory,a new dynamic analysis of a class of damped SD oscillators is presented in this paper.The KCC geometric invariants of SD oscillator in smooth and non-smooth cases are given respectively.The results show that the geometric quantities in the non-smooth case cannot be directly derived from the geometric quantities in the smooth case.Based on these geometric quan-tities,the KCC stability of the SD oscillator at any point of the trajectory in smooth and non-smooth cases is analyzed respectively.The numerical results show that in some regions that deviate from the equilibrium point of the system,the system will show complex dynamic behavior due to small changes in parameters.This study shows that KCC theory can also analyze non-smooth systems to a certain extent.关键词
SD振子/Lyapunov稳定性/Jacobi稳定性/非平衡区域/动力学行为Key words
SD oscillator/Lyapunov stability/Jacobi stability/non-equilibrium region/dynamic behavior分类
数理科学引用本文复制引用
李润红,韦煜明..一类带阻尼SD振子的Jacobi分析[J].曲阜师范大学学报（自然科学版）,2025,51(4):38-48,11.基金项目
广西自然科学基金(2023GXNSFAA026246). （2023GXNSFAA026246）
