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Flunkert, V., Fisher, I. and Scröll, E. (2013) Dynamics, Control and Information in Delayed-Coupled Systems. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 371, 1-4.
https://doi.org/10.1098/rsta.2012.0465

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.