Abstract
Applying a new result for studying the periodic orbits of a differential system via the averaging theory, we provide the first analytic proof of the existence of a Hopf-zero bifurcation for the Michelson system x=y,y=z,z= c2-y-x22, at c=0. Moreover our method estimates the shape of this periodic orbit as a function of c>0, sufficiently small. © 2010 Elsevier Ltd. All rights reserved.
Original language | English |
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Pages (from-to) | 1650-1653 |
Journal | Nonlinear Analysis: Real World Applications |
Volume | 12 |
DOIs | |
Publication status | Published - 1 Jun 2011 |
Keywords
- Averaging method
- Hopf bifurcation
- Michelson system
- Periodic orbit