Nonexistence of ultra-subharmonic periodic orbits in periodically forced differential equation

• 来源期刊: 中国物理（英文版）
• 关键词: nonlinear dynamic system higher-order Melnikov method ultra-subharmonic periodic solution Poincaré map
• 年，卷（期）: 2005,（7）
• 页码范围: 1365-1369
• 页数: 5页
• 语种: 英文

摘要

It is proved that if there exists a periodic solution for a class of non-autonomous differential dynamic systems, it can only be subharmonic, ultra-subharmonic periodic solution is impossible. Moreover, the existence of R-type ultrasubharmonic periodic solution defined for a specified planar system is also denied. As an application of the above conclusions, through investigating some typical examples, it is pointed out that the existence of ultra-subharmonic periodic orbits in a planar perturbation system cannot be determined by second-order Melnikov method. An explanation is also provided.