Triple-Zero Bifurcation of Van Der Pol Oscillator with Delay Feedback
Open Access
- 1 January 2021
- journal article
- research article
- Published by Scientific Research Publishing, Inc. in International Journal of Modern Nonlinear Theory and Application
- Vol. 10 (03), 106-118
- https://doi.org/10.4236/ijmnta.2021.103008
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.Keywords
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