Duffing-Type Oscillator with a Bounded from above Potential in the Presence of Saddle-Center Bifurcation and Singular Perturbation: Frequency Control
We analyze the dynamics of the forced singularly perturbed differential equations of Duffing’s type with a potential that is bounded from above. We explain the appearance of the large frequency nonlinear oscillations of the solutions. It is shown that the frequency can be controlled by a small param...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/848613 |
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| _version_ | 1832556964999069696 |
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| author | Robert Vrabel Pavol Tanuska Pavel Vazan Peter Schreiber Vladimir Liska |
| author_facet | Robert Vrabel Pavol Tanuska Pavel Vazan Peter Schreiber Vladimir Liska |
| author_sort | Robert Vrabel |
| collection | DOAJ |
| description | We analyze the dynamics of the forced singularly perturbed differential equations of Duffing’s type with a potential that is bounded from above. We explain the appearance of the large frequency nonlinear oscillations of the solutions. It is shown that the frequency can be controlled by a small parameter at the highest derivative. |
| format | Article |
| id | doaj-art-930b012b73ea4e64867983a261f09759 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-930b012b73ea4e64867983a261f097592025-02-03T05:43:55ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/848613848613Duffing-Type Oscillator with a Bounded from above Potential in the Presence of Saddle-Center Bifurcation and Singular Perturbation: Frequency ControlRobert Vrabel0Pavol Tanuska1Pavel Vazan2Peter Schreiber3Vladimir Liska4Faculty of Materials Science and Technology, Slovak University of Technology in Bratislava, Hajdoczyho 1, 917 01 Trnava, SlovakiaFaculty of Materials Science and Technology, Slovak University of Technology in Bratislava, Hajdoczyho 1, 917 01 Trnava, SlovakiaFaculty of Materials Science and Technology, Slovak University of Technology in Bratislava, Hajdoczyho 1, 917 01 Trnava, SlovakiaFaculty of Materials Science and Technology, Slovak University of Technology in Bratislava, Hajdoczyho 1, 917 01 Trnava, SlovakiaFaculty of Materials Science and Technology, Slovak University of Technology in Bratislava, Hajdoczyho 1, 917 01 Trnava, SlovakiaWe analyze the dynamics of the forced singularly perturbed differential equations of Duffing’s type with a potential that is bounded from above. We explain the appearance of the large frequency nonlinear oscillations of the solutions. It is shown that the frequency can be controlled by a small parameter at the highest derivative.http://dx.doi.org/10.1155/2013/848613 |
| spellingShingle | Robert Vrabel Pavol Tanuska Pavel Vazan Peter Schreiber Vladimir Liska Duffing-Type Oscillator with a Bounded from above Potential in the Presence of Saddle-Center Bifurcation and Singular Perturbation: Frequency Control Abstract and Applied Analysis |
| title | Duffing-Type Oscillator with a Bounded from above Potential in the Presence of Saddle-Center Bifurcation and Singular Perturbation: Frequency Control |
| title_full | Duffing-Type Oscillator with a Bounded from above Potential in the Presence of Saddle-Center Bifurcation and Singular Perturbation: Frequency Control |
| title_fullStr | Duffing-Type Oscillator with a Bounded from above Potential in the Presence of Saddle-Center Bifurcation and Singular Perturbation: Frequency Control |
| title_full_unstemmed | Duffing-Type Oscillator with a Bounded from above Potential in the Presence of Saddle-Center Bifurcation and Singular Perturbation: Frequency Control |
| title_short | Duffing-Type Oscillator with a Bounded from above Potential in the Presence of Saddle-Center Bifurcation and Singular Perturbation: Frequency Control |
| title_sort | duffing type oscillator with a bounded from above potential in the presence of saddle center bifurcation and singular perturbation frequency control |
| url | http://dx.doi.org/10.1155/2013/848613 |
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