%0 Journal Article
%T Triple-Zero Bifurcation of Van Der Pol Oscillator with Delay Feedback
%A Suqi Ma
%J International Journal of Modern Nonlinear Theory and Application
%P 106-118
%@ 2167-9487
%D 2021
%I Scientific Research Publishing
%R 10.4236/ijmnta.2021.103008
%X 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.
%K Triple-Zero Bifurcation
%K Homoclinic Solutions
%K DDEs
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=111115