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Triple-Zero Bifurcation of Van Der Pol Oscillator with Delay Feedback
Department of Mathematics, China Agricultural University, Beijing, China
- 1 Department of Mathematics, China Agricultural University, Beijing, China
International Journal of Modern Nonlinear Theory and Application·Volume 10 (2021)·Pages 106–118·Published 14 July 2021·DOI10.4236/ijmnta.2021.103008
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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.
KeywordsTriple-Zero BifurcationHomoclinic SolutionsDDEs
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