摘要
研究具有三次非线性时滞项的van der Pol 型时滞系统随两参数( 时滞量和增益系数) 余维一Hopf 分岔,说明了线性化特征方程随两参数变化时的根的分布和Hopf 分岔存在性;通过构造中心流形并且使用范式方法确定出Hopf 分岔的方向以及周期解的稳定性;分析了时滞量对所论系统发生Hopf
Studies the co dimension 1 Hopf bifurcation and its stability in a van der Pol time delay system with cubic nonlinearity. The distribution of roots of its characteristic equation is given with two parameters(time delay and amplitude) varying. The existence of Hopf bifurcation is proved. The direction of Hopf bifurcation and the stability of the periodic solution are determined by constructing the center manifold and using the normal form. The influence of the time delay on Hopf bifurcation is investigated.
出处
《固体力学学报》
CAS
CSCD
北大核心
1999年第4期297-302,共6页
Chinese Journal of Solid Mechanics
基金
国家自然科学基金!( 批准号:19602003)
关键词
非线性时滞系统
HOPF分岔
非线性动力学
nonlinear time delay system, functional differential equation, Hopf bifurcation, normal form, nonlinear dynamics
