Bazı biyolojik modellemelerde fark denklemlerinin kullanımı ve denklemlerin kararlılığı
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Date
2020
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Hatay Mustafa Kemal Üniversitesi
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info:eu-repo/semantics/openAccess
Abstract
Bu tezde diferansiyel denklemler ve fark denklemlerinin bazı biyolojik modellemelerde kullanılması ve kararlılıkları incelenmiştir. Çalışma dört bölümden oluşmuştur. İlk bölümde genel tanımlara ve önceki çalışmalara değinilmiştir. İkinci bölümde temel tanım ve teoremler verilmiş, örneklerle desteklenmiştir. Üçüncü bölümde kararlılık teorisi, diferansiyel ve fark denklemlerinde kararlılık konuları yer almıştır. Dördüncü bölümde ise fark denklemlerinde de Wit modeline dayanan iki bitki türü rekabetinin kararlılık şartları belirlenmiş, diferansiyel denklemlerde ise sınırlı bir alanda bulunan ve yiyecek rekabeti olan iki tür için lojistik denklem yardımıyla matematiksel modelleme oluşturulması ve bazı sabitler için modelin kararlılık kriterleri incelenmiştir
In this thesis, the use of differential equations and difference equations in some biological models and their stability are examined. The study consists of four chapters. In the first part, general definitions and previous studies are mentioned. In the second chapter, basic definitions and theorems are given and supported with examples. In the third part, stability theory, stability of difference equations and stability of differential equations are given. In the fourth chapter, stability conditions of two plant species competitions based on de Wit model were determined in difference equations and in differential equations mathematical modelling was created for two species in a limited area with food competition and the stability criteria of the model for some constants were examined.
In this thesis, the use of differential equations and difference equations in some biological models and their stability are examined. The study consists of four chapters. In the first part, general definitions and previous studies are mentioned. In the second chapter, basic definitions and theorems are given and supported with examples. In the third part, stability theory, stability of difference equations and stability of differential equations are given. In the fourth chapter, stability conditions of two plant species competitions based on de Wit model were determined in difference equations and in differential equations mathematical modelling was created for two species in a limited area with food competition and the stability criteria of the model for some constants were examined.
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Matematik, Mathematics
