Nonexistence of ultra-subharmonic periodic orbits in periodically forced differential equation
Gao Jing-Wu (高经武)ab, Li Qing-Shi(李庆士)a
a Institute of Applied Mechanics, Taiyuan University of Technology, Taiyuan 030024, China; b Department of Physics, Shanxi Datong University, Datong 037009, China
Abstract 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 ultra-subharmonic 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.
Received: 22 December 2003
Revised: 15 December 2004
Accepted manuscript online:
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