吉林大学学报（理学版）Issue(3)：383-388,6.DOI:10.13413/j.cnki.jdxblxb.2015.03.07
拟周期平面振子平衡点的稳定性
Stability of the Equilibrium of Quasi-periodic Planar Oscillator
摘要
Abstract
We generalized the stability criteria for the equilibrium of the periodic system to those for that of quasi-periodic system,applying the method of main integration.Concretely,we showed the stability for the equilibrium x =x′= 0 of the quasi-periodic second order differential equation x″+h(t)x′+a(t)x 2n+1 +e(t,x)=0,n≥1,where h(t),a (t),e (t,x )are quasi-periodic coefficients,whose frequency vectors meet the requirements proposed by Diophantine. And moreover, e(t,x) =O(x 2n+2 )near x = x′= 0.The results we obtained also imply that,under some conditions,the equilibrium of the quasi-periodic oscillator with damping changing sign can still be stable.关键词
拟周期/Diophantine 条件/平衡点稳定性Key words
quasi-periodic/Diophantine condition/stability of the equilibrium分类
数理科学引用本文复制引用
邢秀梅,任秀芳..拟周期平面振子平衡点的稳定性[J].吉林大学学报（理学版）,2015,(3):383-388,6.基金项目
国家自然科学基金(批准号:21364016)、新疆维吾尔自治区自然科学基金(批准号:20122111328)和新疆维吾尔自治区重点学科项目(批准号:2012ZDXK13) （批准号:21364016）
