Stability of autonomous and non autonomous differential equations
| dc.contributor.author | Obi, Olivia Ada | |
| dc.date.accessioned | 2014-09-19T10:40:58Z | |
| dc.date.available | 2014-09-19T10:40:58Z | |
| dc.date.issued | 2013-09 | |
| dc.description | Master of Science in Mathematics. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2013. Supervisor: Assoc. Prof. Dr. Sonuç Zorlu Oğurlu. | en_US |
| dc.description.abstract | ABSTRACT: In this thesis, we dealt with Autonomous and non Autonomous systems of ordinary differential equations and the stability properties of their solutions were discussed with some basic results. We also discussed and analyzed methods of investigating the stability of nonlinear systems and classified equilibrium points (critical points) of linear systems with respect to their stability. Liapounov's direct method for stability of Autonomous and non Autonomous Equations was analyzed in detail. Some important Ecological applications such as Lotka-Volterra Competition Model and Predator-Prey Model modeled by differential Equations were discussed in details with relevant examples. Keywords : Autonomous and Non Autonomous differential equations, Stability, Predator-prey Model, Equilibrium points, Liapounov's Direct Method. ………………………………………………………………………………………………………………………………………………………………………………………………………… ÖZ : Bu tezde, otonom ve otonom olmayan adi difransiyel denklem sistemleri ve bu sistemlerin çözümlerinin stabilite özellikleri tartışılmıştır. Ayrıca, doğrusal olmayan sistemlerin stabilitesi üzerine bazı metodlar çalışılmış ve analiz edilmiş ve doğrusal sistemlerin stabilite özelliklerine göre denge noktaları sınıflandırılmıstır. Otonom ve otonom olmayan denklemlerin stabilitesi için Lyapounov Direkt metodu detaylı bir şekilde analiz edilmiştir. Son olarak, diferansiyel denklemlerce modellenmiş olan Lotka-Volterra Yarışma modeli ve Predator Prey modeli gibi bazı önemli ekolojik uygulamalar ayrıntılı bir şekilde incelenmiştir. Anahtar Kelimeler : Otonom ve otonom olmayan diferansiyel denklemler, Stabilite, Predator-Prey Model, Denge Noktaları, Liapounov Direkt Metod. | en_US |
| dc.identifier.citation | Obi, Olivia Ada. (2013). Stability of autonomous and non autonomous differential equations. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus. | en_US |
| dc.identifier.uri | https://hdl.handle.net/11129/1342 | |
| dc.language.iso | en | |
| dc.publisher | Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ) | en_US |
| dc.relation.publicationcategory | Tez | |
| dc.subject | Mathematics | en_US |
| dc.subject | Differential Equations | en_US |
| dc.subject | Autonomous and Non Autonomous Differential Equations, Stability, Predator-prey Model, Equilibrium Points, Liapounov's Direct Method | en_US |
| dc.title | Stability of autonomous and non autonomous differential equations | en_US |
| dc.type | Thesis |
