Triple-Zero Bifurcation of Van Der Pol Oscillator with Delay Feedback ()
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.
Share and Cite:
Ma, S. (2021) Triple-Zero Bifurcation of Van Der Pol Oscillator with Delay Feedback.
International Journal of Modern Nonlinear Theory and Application,
10, 106-118. doi:
10.4236/ijmnta.2021.103008.
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