TY - JOUR
T1 - Local Bifurcation Cyclicity for a Non-Polynomial System
AU - Huang , Wenhui
AU - Yao , Jie
AU - Wang , Qinlong
JO - Journal of Nonlinear Modeling and Analysis
VL - 4
SP - 1431
EP - 1445
PY - 2025
DA - 2025/07
SN - 7
DO - http://doi.org/10.12150/jnma.2025.1431
UR - https://global-sci.org/intro/article_detail/jnma/24244.html
KW - Non-polynomial system, quasi-Lyapunov constant, nilpotent singularity, Hopf bifurcation.
AB - <p style="text-align: justify;">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.</p>