Novel Hyperbolic Homoclinic Solutions of the Helmholtz-Duffing Oscillators
The exact and explicit homoclinic solution of the undamped Helmholtz-Duffing oscillator is derived by a presented hyperbolic function balance procedure. The homoclinic solution of the self-excited Helmholtz-Duffing oscillator can also be obtained by an extended hyperbolic perturbation method. The ap...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2016-01-01
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| Series: | Shock and Vibration |
| Online Access: | http://dx.doi.org/10.1155/2016/9471423 |
| Summary: | The exact and explicit homoclinic solution of the undamped Helmholtz-Duffing oscillator is derived by a presented hyperbolic function balance procedure. The homoclinic solution of the self-excited Helmholtz-Duffing oscillator can also be obtained by an extended hyperbolic perturbation method. The application of the present homoclinic solutions to the chaos prediction of the nonautonomous Helmholtz-Duffing oscillator is performed. Effectiveness and advantage of the present solutions are shown by comparisons. |
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| ISSN: | 1070-9622 1875-9203 |