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Nonlinear response of a forced van der Pol–Duffing oscillator at non-resonant bifurcations of codimension two
| Content Provider | Semantic Scholar |
|---|---|
| Author | Ji, Jinchen Zhang, Nong |
| Copyright Year | 2009 |
| Abstract | Abstract Non-resonant bifurcations of codimension two may appear in the controlled van der Pol–Duffing oscillator when two critical time delays corresponding to a double Hopf bifurcation have the same value. With the aid of centre manifold theorem and the method of multiple scales, the non-resonant response and two types of primary resonances of the forced van der Pol–Duffing oscillator at non-resonant bifurcations of codimension two are investigated by studying the possible solutions and their stability of the four-dimensional ordinary differential equations on the centre manifold. It is shown that the non-resonant response of the forced oscillator may exhibit quasi-periodic motions on a two- or three-dimensional (2D or 3D) torus. The primary resonant responses admit single and mixed solutions and may exhibit periodic motions or quasi-periodic motions on a 2D torus. Illustrative examples are presented to interpret the dynamics of the controlled system in terms of two dummy unfolding parameters and exemplify the periodic and quasi-periodic motions. The analytical predictions are found to be in good agreement with the results of numerical integration of the original delay differential equation. |
| Starting Page | 1467 |
| Ending Page | 1475 |
| Page Count | 9 |
| File Format | PDF HTM / HTML |
| DOI | 10.1016/j.chaos.2008.06.008 |
| Volume Number | 41 |
| Alternate Webpage(s) | https://opus.lib.uts.edu.au/bitstream/10453/8357/1/2008007811.pdf |
| Alternate Webpage(s) | https://doi.org/10.1016/j.chaos.2008.06.008 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
