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Engelborghs, K., Luzyanina, T. and Roose, D. (2002) Numerical Bifurcation Analysis of Delay Differentia, Equations Using DDE-BIFTOOL. ACM Transactions on Mathematical Software (TOMS), 28, 1-21. https://doi.org/10.1145/513001.513002

has been cited by the following article:

• 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.