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Bogdanov–Takens singularity in Van der Pol’s oscillator with delayed feedback

✍ Scribed by Weihua Jiang; Yuan Yuan

Publisher
Elsevier Science
Year
2007
Tongue
English
Weight
917 KB
Volume
227
Category
Article
ISSN
0167-2789

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✦ Synopsis

In this paper, we study the classical Van der Pol's equation with delayed feedback. We investigate the Bogdanov-Takens singularity and bifurcation occurring in the system with the variation of the original parameters by using the normal form method, and predict the suitable choice in the feedback control in order to obtain the asymptotic stable state.

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VAN DER POL'S OSCILLATOR UNDER DELAYED F
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✍ 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

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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