On Using Curvature to Demonstrate Stability
A new approach for demonstrating the global stability of ordinary differential equations is given. It is shown that if the curvature of solutions is bounded on some set, then any nonconstant orbits that remain in the set, must contain points that lie some minimum distance apart from each other. This...
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| Format: | Article |
| Language: | English |
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Wiley
2008-01-01
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| Series: | Differential Equations and Nonlinear Mechanics |
| Online Access: | http://dx.doi.org/10.1155/2008/745242 |
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| _version_ | 1832555381528723456 |
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| author | C. Connell McCluskey |
| author_facet | C. Connell McCluskey |
| author_sort | C. Connell McCluskey |
| collection | DOAJ |
| description | A new approach for demonstrating the global stability of ordinary differential equations is given. It is shown that if the curvature of solutions is bounded on some set, then any nonconstant orbits that remain in the set, must contain points that lie some minimum distance apart from each other. This is used to establish a negative-criterion for periodic orbits. This is extended to give a method of proving an equilibrium to be globally stable. The approach can also be used to rule out the sudden appearance of large-amplitude periodic orbits. |
| format | Article |
| id | doaj-art-6a4e3fa83f2744de97aa38e8cf3fe9b4 |
| institution | Kabale University |
| issn | 1687-4099 1687-4102 |
| language | English |
| publishDate | 2008-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Differential Equations and Nonlinear Mechanics |
| spelling | doaj-art-6a4e3fa83f2744de97aa38e8cf3fe9b42025-02-03T05:48:22ZengWileyDifferential Equations and Nonlinear Mechanics1687-40991687-41022008-01-01200810.1155/2008/745242745242On Using Curvature to Demonstrate StabilityC. Connell McCluskey0Department of Mathematics, Wilfrid Laurier University, 75 University Ave West, Waterloo, ON, N2L 3C5, CanadaA new approach for demonstrating the global stability of ordinary differential equations is given. It is shown that if the curvature of solutions is bounded on some set, then any nonconstant orbits that remain in the set, must contain points that lie some minimum distance apart from each other. This is used to establish a negative-criterion for periodic orbits. This is extended to give a method of proving an equilibrium to be globally stable. The approach can also be used to rule out the sudden appearance of large-amplitude periodic orbits.http://dx.doi.org/10.1155/2008/745242 |
| spellingShingle | C. Connell McCluskey On Using Curvature to Demonstrate Stability Differential Equations and Nonlinear Mechanics |
| title | On Using Curvature to Demonstrate Stability |
| title_full | On Using Curvature to Demonstrate Stability |
| title_fullStr | On Using Curvature to Demonstrate Stability |
| title_full_unstemmed | On Using Curvature to Demonstrate Stability |
| title_short | On Using Curvature to Demonstrate Stability |
| title_sort | on using curvature to demonstrate stability |
| url | http://dx.doi.org/10.1155/2008/745242 |
| work_keys_str_mv | AT cconnellmccluskey onusingcurvaturetodemonstratestability |