Harmonic and subharmonic solutions of the SD oscillator

被引：21
作者：
Chen, Hebai [1 ]
Xie, Jianhua [1 ]
机构：
[1] Southwest Jiaotong Univ, Sch Mech & Engn, Chengdu 610031, Sichuan, Peoples R China
来源：
NONLINEAR DYNAMICS | 2016年 / 84卷 / 04期
基金：
中国国家自然科学基金;
关键词：
Harmonic solution; Subharmonic solution; SD oscillator; PERIODIC-SOLUTIONS; DUFFING EQUATIONS; EXISTENCE; DYNAMICS; SYSTEMS; POINT;
D O I：
10.1007/s11071-016-2659-7
中图分类号：
TH [机械、仪表工业];
学科分类号：
0802 ;
摘要：
In this paper we study the existence and uniqueness of harmonic solutions and subharmonic ones of the smooth-and-discontinuous (SD, for short) differential equation , where and . However, for this oscillator it is easy to find that the known theory cannot be applied directly.
引用
收藏
页码：2477 / 2486
页数：10
相关论文
共 23 条
  • [1] [Anonymous], 1992, An Experimental Approach to Nonlinear Dynamics and Chaos
  • [2] Piecewise linear approach to an archetypal oscillator for smooth and discontinuous dynamics
    Cao, Qingjie
    Wiercigroch, Marian
    Pavlovskaia, Ekaterina E.
    Michael, J.
    Thompson, T.
    Grebogi, Celso
    [J]. PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2008, 366 (1865): : 635 - 652
  • [3] Archetypal oscillator for smooth and discontinuous dynamics
    Cao, Qingjie
    Wiercigroch, Marian
    Pavlovskaia, Ekaterina E.
    Grebogi, Celso
    Thompson, J. Michael T.
    [J]. PHYSICAL REVIEW E, 2006, 74 (04):
  • [4] The existence of subharmonic solutions with prescribed minimal period for forced pendulum equations with impulses
    Chen, Huiwen
    Li, Jianli
    He, Zhimin
    [J]. APPLIED MATHEMATICAL MODELLING, 2013, 37 (06) : 4189 - 4198
  • [5] Harmonic and subharmonic solutions for superlinear damped Duffing equation
    Cheng, Zhibo
    Ren, Jingli
    [J]. NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2013, 14 (02) : 1155 - 1170
  • [6] Sub-harmonic resonant solutions of a harmonically excited dry friction oscillator
    Csernak, G.
    Stepan, G.
    Shaw, S. W.
    [J]. NONLINEAR DYNAMICS, 2007, 50 (1-2) : 93 - 109
  • [7] DEIMLING K, 1994, DIFFER INTEGRAL EQU, V7, P759
  • [8] ON PERIODIC-SOLUTIONS OF SUBLINEAR DUFFING EQUATIONS
    DING, TG
    IANNACCI, R
    ZANOLIN, F
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1991, 158 (02) : 316 - 332
  • [9] DING TG, 1981, CHINESE ANN MATH B, V2, P281
  • [10] DING TG, 1982, SCI SIN A-MATH P A T, V25, P918
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