Bifurcation of Safe Basins and Chaos in Nonlinear Vibroimpact Oscillator under Harmonic and Bounded Noise Excitations
The erosion of the safe basins and chaotic motions of a nonlinear vibroimpact oscillator under both harmonic and bounded random noise is studied. Using the Melnikov method, the system’s Melnikov integral is computed and the parametric threshold for chaotic motions is obtained. Using the Monte-Carlo...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/967395 |
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| author | Rong Haiwu Wang Xiangdong Luo Qizhi Xu Wei Fang Tong |
| author_facet | Rong Haiwu Wang Xiangdong Luo Qizhi Xu Wei Fang Tong |
| author_sort | Rong Haiwu |
| collection | DOAJ |
| description | The erosion of the safe basins and chaotic motions of a nonlinear vibroimpact oscillator under both harmonic and bounded random noise is studied. Using the Melnikov method, the system’s Melnikov integral is computed and the parametric threshold for chaotic motions is obtained. Using the Monte-Carlo and Runge-Kutta methods, the erosion of the safe basins is also discussed. The sudden change in the character of the stochastic safe basins when the bifurcation parameter of the system passes through a critical value may be defined as an alternative stochastic bifurcation. It is founded that random noise may destroy the integrity of the safe basins, bring forward the occurrence of the stochastic bifurcation, and make the parametric threshold for motions vary in a larger region, hence making the system become more unsafely and chaotic motions may occur more easily. |
| format | Article |
| id | doaj-art-2bece1164f154c9293ed44b1b0dbd0ef |
| institution | OA Journals |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-2bece1164f154c9293ed44b1b0dbd0ef2025-08-20T02:04:49ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/967395967395Bifurcation of Safe Basins and Chaos in Nonlinear Vibroimpact Oscillator under Harmonic and Bounded Noise ExcitationsRong Haiwu0Wang Xiangdong1Luo Qizhi2Xu Wei3Fang Tong4Department of Mathematics, Foshan University, Foshan 528000, ChinaDepartment of Mathematics, Foshan University, Foshan 528000, ChinaDepartment of Mathematics, Foshan University, Foshan 528000, ChinaDepartment of Applied Mathematics, Northwestern Polytechnical University, Xi’an 710072, ChinaDepartment of Applied Mathematics, Northwestern Polytechnical University, Xi’an 710072, ChinaThe erosion of the safe basins and chaotic motions of a nonlinear vibroimpact oscillator under both harmonic and bounded random noise is studied. Using the Melnikov method, the system’s Melnikov integral is computed and the parametric threshold for chaotic motions is obtained. Using the Monte-Carlo and Runge-Kutta methods, the erosion of the safe basins is also discussed. The sudden change in the character of the stochastic safe basins when the bifurcation parameter of the system passes through a critical value may be defined as an alternative stochastic bifurcation. It is founded that random noise may destroy the integrity of the safe basins, bring forward the occurrence of the stochastic bifurcation, and make the parametric threshold for motions vary in a larger region, hence making the system become more unsafely and chaotic motions may occur more easily.http://dx.doi.org/10.1155/2014/967395 |
| spellingShingle | Rong Haiwu Wang Xiangdong Luo Qizhi Xu Wei Fang Tong Bifurcation of Safe Basins and Chaos in Nonlinear Vibroimpact Oscillator under Harmonic and Bounded Noise Excitations Journal of Applied Mathematics |
| title | Bifurcation of Safe Basins and Chaos in Nonlinear Vibroimpact Oscillator under Harmonic and Bounded Noise Excitations |
| title_full | Bifurcation of Safe Basins and Chaos in Nonlinear Vibroimpact Oscillator under Harmonic and Bounded Noise Excitations |
| title_fullStr | Bifurcation of Safe Basins and Chaos in Nonlinear Vibroimpact Oscillator under Harmonic and Bounded Noise Excitations |
| title_full_unstemmed | Bifurcation of Safe Basins and Chaos in Nonlinear Vibroimpact Oscillator under Harmonic and Bounded Noise Excitations |
| title_short | Bifurcation of Safe Basins and Chaos in Nonlinear Vibroimpact Oscillator under Harmonic and Bounded Noise Excitations |
| title_sort | bifurcation of safe basins and chaos in nonlinear vibroimpact oscillator under harmonic and bounded noise excitations |
| url | http://dx.doi.org/10.1155/2014/967395 |
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