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Quasiperiodic phenomena in the Van der Pol–Mathieu equation

✍ Scribed by F. Veerman; F. Verhulst

Book ID
104033807
Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
493 KB
Volume
326
Category
Article
ISSN
0022-460X

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✦ Synopsis

The Van der Pol-Mathieu equation, combining self-excitation and parametric excitation, is analysed near and at 1:2 resonance, using the averaging method. We analytically prove the existence of stable and unstable periodic solutions near the parametric resonance frequency. Above a certain detuning threshold, quasiperiodic solutions arise with basic periods of order 1 and order 1= where is the (small) detuning parameter.

📜 SIMILAR VOLUMES

Chaos in Van der Pol's equation
Chaos in Van der Pol's equation
✍ Y.H. Ku; Xiaoguang Sun 📂 Article 📅 1990 🏛 Elsevier Science 🌐 English ⚖ 402 KB

Van der Pal's Equation was first given in 1926. It gives limit cycles. The present paper reports the chaotic behavior of modiJied Van der Pal's Equation with forcing function. In three of six cases, CHAOS is found, while three other cases give limit cycles.