Solution of hilbert sixteenth problem for the cubic lienard and quartic polynomial differential system
Also available in printed version
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| Format: | Doctoral thesis |
| Language: | English |
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Universiti Teknologi Malaysia
2025
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| Online Access: | https://utmik.utm.my/handle/123456789/56074 |
| Abstract | Abstract here |
| _version_ | 1855605635775725568 |
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| author | Hero Waisi Salih |
| author2 | Zainal Abdul Aziz, supervisor |
| author_facet | Zainal Abdul Aziz, supervisor Hero Waisi Salih |
| author_sort | Hero Waisi Salih |
| description | Also available in printed version |
| format | Doctoral thesis |
| id | utm-123456789-56074 |
| institution | Universiti Teknologi Malaysia |
| language | English |
| publishDate | 2025 |
| publisher | Universiti Teknologi Malaysia |
| record_format | DSpace |
| record_pdf | Restricted |
| spelling | utm-123456789-560742025-03-17T19:04:08Z Solution of hilbert sixteenth problem for the cubic lienard and quartic polynomial differential system Hero Waisi Salih Zainal Abdul Aziz, supervisor Science Also available in printed version In the present work, the second part of Hilbert’s sixteenth problem is solved to a certain extent, by using both Lienard system and polynomial differential system. For the Lienard system, the first and second Lyapunov quantities are calculated by the Lyapunov - Poincare method. The Poincare-Bendixon theorem is then used to find the relation between the stability and lower bound of the number of limit cycles of the Lienard system. The averaging theory is used to evaluate the maximum number of limit cycles for the Lienard equation. These results will assist in determining the first integral of the Lienard equation. For the polynomial differential system, the first and second Lyapunov quantities are calculated by using the Lyapunov technique in Euclidean space, and then the bifurcation of one limit cycle is investigated at infinity for a class of system of homogeneous polynomials of degree four. The problem for bifurcation of limit cycles from infinity is converted from the original system to the class of complex autonomous differential system. By computing the of singular point values, the conditions of the origin to be a center and the highest finite degree foci are obtained. Letting the normal parameters to be of constant values, a quartic system which bifurcates one limit cycle from infinity is constructed. Finally, from the application of the nanoparticle model, the associated first and second Lyapunov quantities of the model are computed by using the Lyapunov - Poincare method, the first integral of the system is established, and these imply that the model equations are stable under the given initial and boundary conditions. Physically this means that the nanoparticle system in the plane is stable, where in the process the materials become nanoparticle by heating and freezing. The limit cycles in the system are found to be non-existent, which physically means that the time for heating and freezing of materials is not periodic snhas UTM 203 p. Thesis (Ph.D (Matematik)) - Universiti Teknologi Malaysia, 2015 2025-03-17T04:19:30Z 2025-03-17T04:19:30Z 2015 Doctoral thesis https://utmik.utm.my/handle/123456789/56074 valet-20170214-121441 vital:95451 ENG Closed Access UTM Complete Unpublished application/pdf Universiti Teknologi Malaysia |
| spellingShingle | Science Hero Waisi Salih Solution of hilbert sixteenth problem for the cubic lienard and quartic polynomial differential system |
| thesis_level | PhD |
| title | Solution of hilbert sixteenth problem for the cubic lienard and quartic polynomial differential system |
| title_full | Solution of hilbert sixteenth problem for the cubic lienard and quartic polynomial differential system |
| title_fullStr | Solution of hilbert sixteenth problem for the cubic lienard and quartic polynomial differential system |
| title_full_unstemmed | Solution of hilbert sixteenth problem for the cubic lienard and quartic polynomial differential system |
| title_short | Solution of hilbert sixteenth problem for the cubic lienard and quartic polynomial differential system |
| title_sort | solution of hilbert sixteenth problem for the cubic lienard and quartic polynomial differential system |
| topic | Science |
| url | https://utmik.utm.my/handle/123456789/56074 |
| work_keys_str_mv | AT herowaisisalih solutionofhilbertsixteenthproblemforthecubiclienardandquarticpolynomialdifferentialsystem |