Local Bifurcation Cyclicity for a Non-Polynomial System (Journal of Nonlinear Modeling and Analysis, 2025)
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 specificsystems from the original model are transformed into two equivalent infinitepolynomial systems, and the highest order of fine focus as the nilpotent Hopfbifurcation or Hopf bifurcation point is determined respectively. At the sametime, the local bifurcation cyclicities and center problems for two systems aresolved respectively. To our knowledge, such dynamic properties are rarelyanalyzed in many non-polynomial models.
Keywords: Non-polynomial system; quasi-Lyapunov constant; nilpotent singularity; Hopf bifurcation.