Monotone Discontinuous Dynamical Systems And Applications

Date

2012-12-31

Author

Akhmet, Marat

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Tarih boyunca diferansiyel denklemlerde monoton methodların uygulamları ve karşılaştırma argümanları üzerine birçok çalışma yapılmıştır.Müller (1926) ve Kamke(1932) adlı matematikçilerimizin çalışmaları bu alanın kurucularındandır.Monoton dinamik sistemler, sıralı metrik system üzerine kurulmuş, sıralı başlangıç durumunu sıralı sonraki duruma götüren dinamik sistemdir. Daha ayrıntılı inceleyecek olursak monoton dinamik sistemler bize bir düzeneğin başlangıç koşulunu bildiğimiz durumlarda daha sonraki durumlarda hangi konumda bulunacağımız hakkında bilgi vermektedir. Monoton dinamik sistemler ve uygulamaları yıllarca diferansiyel denklemlerde kullanılmıştır. Monoton dinamik sistemler uzun yıllarca sürekli dinamik sistemler üzerinde incelenmiştir. Ama sureli zamanlı monoton dinamik sistemlerde ve bilhassa rekabetçi ve kooperatif diferansiyel denklemlerde henüz yeni ilerlemeler yoktur. Monoton dinamik sistemler günümüz uygulamalarında kullanışlı bir araç olacaktır. Monoton dinamik sistemlerin sıralılık özelliği başlangıç koşullarını bildiğimiz bir sistemin ileriki devrelerde nasıl ilerleyeceği hakkında bilgi verecektir. Monotone süreksiz dinamik sistemleri incelediğimizde ise bize daha gerçekçi veriler sunacaktır. Ayrıca uygulamaları reaksiyon ve difüzyon sistemlerinde de kullanılmaktadır.Monoton dinamik sistemlerin uygulama alanları olarak yarış ve göç alan ekosistemlerin incelenmesi,biyokimyasal kontrol çemberi gibi alanlarda uygulamaları bulunmaktadır.Smale’in rekabetçi sistemler için matematiksel modeli bulunmaktadır.. Bu proje çerçevesinde Birinci yıl • Sonuçları öğrenmek • Teoriyi geliştirmek İkinci yıl; • Monoton süreksiz dinamik sistem özellikleri inceleme Üçüncü yıl; • Elde ettiğimiz teorik verileri uygulamak

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https://hdl.handle.net/11511/58638

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Department of Mathematics, Project and Design

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Citation Formats

M. Akhmet, “Monotone Discontinuous Dynamical Systems And Applications,” 2012. Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/58638.