Abstract
Investigating limit cycle oscillator with extended delay feedback is an efficient way to understand the dynamics of a global coupled ensemble or a large system with periodic oscillation. The stability and bifurcation of the arisen neutral equation are obtained. Stability switches and Hopf bifurcations appear when delay passes through a sequence of critical values. Global continuation of Hopf bifurcating periodic solutions and double{Hopf bifurcation are studied. With the help of the unfolding system near double{Hopf bifurcation obtained by using method of normal forms, quasiperiodic oscillations are found. The number of the coexisted periodic solutions is estimated. Finally, some numerical simulations are carried out.
| Original language | English |
|---|---|
| Pages (from-to) | 1439-1458 |
| Number of pages | 20 |
| Journal | Discrete and Continuous Dynamical Systems - Series B |
| Volume | 18 |
| Issue number | 5 |
| DOIs | |
| State | Published - Jul 2013 |
Keywords
- Double Hopf bifurcation
- Extended delay feedback
- Limit cycle oscillator
- Neutral type
- Quasiperiodic solution
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