TITLE:
Triple-Zero Bifurcation of Van Der Pol Oscillator with Delay Feedback
AUTHORS:
Suqi Ma
KEYWORDS:
Triple-Zero Bifurcation, Homoclinic Solutions, DDEs
JOURNAL NAME:
International Journal of Modern Nonlinear Theory and Application,
Vol.10 No.3,
August
6,
2021
ABSTRACT: A van der Pol equation underlying state feedback control is investigated and the triple-zero bifurcation arises at the bifurcation point which is of codimension three singularity. By applying Schmidt-Lyapunov reduction method combined with center manifold analytical technique, the near approximating formal norm is derived at the triple-zero point. Hence after, as varying parameters continuously, the numerical simulation produces homoclinic bifurcation solutions appearing in system. In addition, the numerical simulation also exhibits the produced double-period limit cycle with chosen bifurcation parameters and the routes to chaos via period-doubling bifurcation are also verified.