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| Local Bifurcation Cyclicity for a Non-polynomial System |
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| KeyWord:Non-polynomial system, quasi-Lyapunov constant, nilpotent singularity, Hopf bifurcation |
| Author Name | Affiliation | | Wenhui Huang | School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541004, China | | Jie Yao | School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541004, China | | Qinlong Wang | School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541004, China
Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation $\&$ Center for Applied Mathematics of Guangxi (GUET\&GXNU), Guilin 541002, China |
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| Abstract: |
| In this paper, we propose a class of general non-polynomial analytic oscillator models, and study the limit cycle bifurcation at the nilpotent singularity or elementary center-focus. By Taylor expansion, two specific systems from the original model are transformed into two equivalent infinite polynomial systems, and the highest order of fine focus as the nilpotent Hopf bifurcation or Hopf bifurcation point is determined respectively. At the same time, the local bifurcation cyclicities and center problems for two systems are solved respectively. To our knowledge, such dynamic properties are rarely analyzed in many non-polynomial models. |
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