Double Hopf Bifurcation with Strong Resonances in Delayed Systems with Nonlinerities
An efficient method is proposed to study delay-induced strong resonant double Hopf bifurcation for nonlinear systems with time delay. As an illustration, the proposed method is employed to investigate the 1 : 2 double Hopf bifurcation in the van der Pol system with time delay. Dynamics arising from...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2009-01-01
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| Series: | Mathematical Problems in Engineering |
| Online Access: | http://dx.doi.org/10.1155/2009/759363 |
| Summary: | An efficient method is proposed to study delay-induced strong resonant double Hopf bifurcation for nonlinear systems with time delay. As an illustration, the proposed method is employed to investigate the 1 : 2 double Hopf bifurcation in the van der Pol system with time delay. Dynamics arising from the bifurcation are classified qualitatively and expressed approximately in a closed form for either square or cubic nonlinearity. The results show that 1 : 2 resonance can lead to codimension-three and codimension-two bifurcations. The validity of analytical predictions is shown by their consistency with numerical simulations. |
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| ISSN: | 1024-123X 1563-5147 |