dc.contributor.author |
Savun, İpek |
|
dc.date.accessioned |
2012-12-13T14:20:38Z |
|
dc.date.available |
2012-12-13T14:20:38Z |
|
dc.date.issued |
2010 |
|
dc.identifier.citation |
Savun, Ipek. (2010). Stability of Systems of Differential Equations and Biological Applications. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus. |
en_US |
dc.identifier.uri |
http://hdl.handle.net/11129/220 |
|
dc.description |
Master of Science in Mathematics. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2010. Supervisor: Assoc. Prof. Dr. Svitlana Rogovchenko. |
en_US |
dc.description.abstract |
ABSTRACT: In this thesis, we deal with systems of ordinary differential equations and discuss the stability properties of their solutions. We classify equilibrium points of linear systems with respect to their type and stability and discuss the methods for investigating the stability properties of nonlinear systems. Existence of periodic solutions which plays an important role in stability theory is also discussed. In addition, some important ecological applications, such as Lotka-Volterra predator-prey model, competition model and nutrient-prey-predator model with intratrophic predation, modeled by the systems of differential equations are also considered. Recent results obtained for these applications are also included.
Keywords: Stability, Periodic solution, Predator-prey model, Intratrophic predation.
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ÖZ: Bu tezde, birinci dereceden denklem sistemleri ve sistemlerin çöozümlerinin kararlılığı üzerinde çalıştık. Lineer sistemlerin kritik noktalarını türlerine ve kararlılıklarına göre sınıflandırdık, lineer olmayan sistemlerin kararlılık özelliklerini inceleyen metodları ele aldık. Çözümlerin kararlılık analizinde önemli rol oynayan periyodik çözümlerin varlığı üzerinde çalıştık. Bunlara ek olarak, diferansiyel denklemlerle ifade edilebilen bazı önemli ekolojik uygulamaları inceledik. Örneğin; Lotka-Volterra av-avcı ilişki modeli, türler arası rekabet modeli ve intratropik avlanma etkisindeki besin-av-avcı modeli. Bu uygulamalarla ilgili elde edilen yeni sonuçlara da yer verdik.
Anathar Kelimeler: Kararlılık, Periodik çözüm, Av-avcı ilişkisi, Intratropik avlanma. |
en_US |
dc.language.iso |
en |
en_US |
dc.publisher |
Eastern Mediterranean University (EMU) |
en_US |
dc.subject |
Mathematics |
en_US |
dc.subject |
Stability - Periodic Solution - Predator-Prey Model - Intratrophic Predation |
en_US |
dc.title |
Stability of Systems of Differential Equations and Biological Applications |
en_US |
dc.type |
Thesis |
en_US |