%0 Journal Article
%T Nonexistence of ultra-subharmonic periodic orbits in periodically forced differential equation<br>周期激励微分方程中超次谐周期轨道的不存在性
%A Gao Jing-Wu
%A Li Qing-Shi
%A <br>高经武
%A 李庆士
%J 中国物理 B
%D 2005
%I 
%X 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.
%K nonlinear dynamic system
%K higher-order Melnikov method
%K ultra-subharmonic periodic solution
%K Poincar\'{e} map<br>非线性动力系统，二阶Melnikov方法，超次谐周期轨道，Poincaré映射
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=6E709DC38FA1D09A4B578DD0906875B5B44D4D294832BB8E&cid=47EA7CFDDEBB28E0&jid=CD8D6A6897B9334F09D8D1648C376FB4&aid=FD181B1B25A8CF09E25FED15D4CD9CA4&yid=2DD7160C83D0ACED&vid=F3583C8E78166B9E&iid=DF92D298D3FF1E6E&sid=995E04834DE9F169&eid=01471B003B2963CC&journal_id=1009-1963&journal_name=中国物理&referenced_num=0&reference_num=10