Abstract
In this paper, a modified averaging scheme is presented for a class of time-delayed vibration systems with slow variables. The new scheme is a combination of the averaging techniques proposed by Hale and by Lehman and Weibel, respectively. The averaged equation obtained from the modified scheme is simple enough but it retains the required information for the local nonlinear dynamics around an equilibrium. As an application of the present method, the delay value for which a secondary Hopf bifurcation occurs is successfully located for a delayed van der Pol oscillator.
| Original language | English |
|---|---|
| Pages (from-to) | 449-454 |
| Number of pages | 6 |
| Journal | Acta Mechanica Sinica/Lixue Xuebao |
| Volume | 24 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - Aug 2008 |
| Externally published | Yes |
Keywords
- Secondary Hopf bifurcation
- The averaging technique
- Time delay
- Van der Pol oscillator