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Zero-Hopf bifurcation for van der Pol’s oscillator with delayed feedback

✍ Scribed by Xiaoqin Wu; Liancheng Wang

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
394 KB
Volume
235
Category
Article
ISSN
0377-0427

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✦ Synopsis

In this paper, we study the dynamical behaviors of the following van der Pol oscillator with delay

In the case that its associated characteristic equation has a simple zero root and a pair of purely imaginary roots (zero-Hopf singularity), the normal form is obtained by performing a center manifold reduction and by using the normal form theory developed by Faria and

  1. is obtained to predict the bifurcation diagrams from which saddle-node bifurcation, pitchfork bifurcation, Hopf bifurcation (the existence and stability of the periodic solutions), and heteroclinic bifurcation are determined. Some examples are given to confirm the theoretical results.

📜 SIMILAR VOLUMES

VAN DER POL'S OSCILLATOR UNDER DELAYED F
VAN DER POL'S OSCILLATOR UNDER DELAYED FEEDBACK
✍ F.M. Atay 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 171 KB

The effect of delayed feedback on oscillatory behaviour is investigated for the classical van der Pol oscillator. It is shown how the presence of delay can change the amplitude of limit cycle oscillations, or suppress them altogether. The result is compared to the conventional proportional-and-deriv