1:2内共振Hopf-Hopf系统的多脉冲跳跃轨道和同宿树  

MULTI-PLUSE ORBITS AND HOMOCLINIC TREES IN HOPF-HOPF SYSTEMS WITH 1:2 INTERNAL RESONANCE

作　　者：梁建术[1] 陈予恕[1] 

机构地区：[1]天津大学机械学院,天津300072

出　　处：《机械强度》2002年第2期190-195,201,共7页Journal of Mechanical Strength

基　　金：国家自然科学基金资助项目 (重大 1 9990 51 0 );国家重点基础研究专项经费资助 (G1 9980 2 0 31 6) ;博士点基金资助 (D0 990 1 )

摘　　要：根据能量差函数、能量序列以及脉冲序列 ,研究 1:2两自由度系统在哈密顿摄动和非哈密顿摄动情况下的多脉冲跳跃轨道和同宿树。研究表明在无阻尼情况 ,存在多脉冲Smale马蹄型 ;在有阻尼情况 ,在简约耗散系统中两个不稳定平衡点之间存在着多脉冲跳跃异宿轨道。在两种情况下存在着描述多脉冲解反复分岔的同宿树。According to energy difference functions, energy sequence and pulse sequence, multi pulse orbits and homoclinic trees in Hopf Hopf systems with 1:2 internal resonance were investigated, under Hamiltonian resonance and non Hamiltonian resonance. The results show that there exists pulse Smale horseshoes in the case of no damping, and multi pulse jumping hteroclinic orbit between of two unstable fixed points of reduced system in the dissipative case. In both cases, one can find homiclinic trees, which describe the repeated bifurcations of multi pulse solutions. Numerical simulations verified the results of theoretical analysis.

关 键 词：Hopf-Hopf 多脉冲 同宿树 异宿轨道 内共振 非线性动力系统 

分 类 号：O322[理学—一般力学与力学基础]