Yaygın Olarak Kullanılan Büyüme Modellerinin Genelleştirilmesi Üzerine Bir Çalışma

Abstract

Bu tezde yaygın olarak kullanılan büyüme modellerinin genelleştirilmesi sunulmuştur. () () t f t rf t ′ = hız-durum adi diferansiyel denkleminin daha genel bir çözümü olarak Koya-Goshu biyolojik büyüme modeli tanıtılmaktadır. Koya-Goshu modeli, biri büyüme durumunu ve diğeri asimptotik davranışları etkileyen iki parametreden oluşur. Burada, Koya-Goshu modeli ile Brody, Von Bertalanffy, Richards, Weibull, Monomoleküler, Mitscherlich, Gompertz, Klasik Lojistik, Genelleştirilmiş Lojistik ve Genelleştirilmiş Lojistik Fonksiyonunun Özel Durumu gibi yaygın olarak kullanılan büyüme modellerinin arasındaki matematiksel ilişkiler ayrıntılı olarak incelenerek, bir akış şemasında gösterilmiştir. Bu büyüme modeli öyle esnektir ki, şimdiye kadar hiç kullanılmamış yeni yararlı modeller üretme kapasitesine de sahiptir. Bunun yanında yukarıda adı geçen büyüme modelleri ele alınarak her birinin biyolojik büyümeleri tanımlayan hız-durum diferansiyel denkleminin bir çözümünün olduğu açıkça belirtilmektedir. Hız-durum denkleminin çözümleri olarak nispi büyüme oran fonksiyonları ve büyümeleri incelenmiştir. Yukarıda belirtilen fonksiyonlar için nispi büyüme fonksiyonu tr , İntegral Sabiti logC ve B parametresi oluşturuldu. Modellerin türevleri, bu türevlerin literatürde bulunamaması ve biyoloji bilimleri alanlarında çalışan matematik dışı çalışmacılar da düşünülerek ayrıntılı olarak sunulmaktadır.,In this thesis, generalization of widely used growth models is presented. The KoyaGoshu biological growth models is introduced as a more general solution of the speed-state ordinary differential equation () () t f t rf t ′ = . The Koya-Goshu model consists of two parameters, one affecting the growth state and the other asymptotic behavior. Here, the mathematical relationships between the Koya-Goshu model and the widely used growth models such as Brody, Von Bertalanffy, Richards, Weibull, Monomolecular, Mitscherlich, Gompertz, Classical Logistic, Generalized Logistic Function and the special situation of the Logistic Function are examined in detail and shown in a flowchart. This growth model is so flexible that it has the capacity to produce new useful models that have never been used. In addition, the mentioned growth models above are considered and it is clearly stated that each one has a solution of the speed-state differential equation describing the biological growth. Relative growth rate functions and their growth are examined as solutions of the velocity-state equation. The relative growth function tr , the Integral Constant logC and the parameter B were created for the functions described above. Derivatives of the models are presented in detail considering non-mathematics researchers working in the fields of biology and unavailability of these derivatives in literature.

In this thesis, generalization of widely used growth models is presented. The KoyaGoshu biological growth models is introduced as a more general solution of the speed-state ordinary differential equation () () t f t rf t ′ = . The Koya-Goshu model consists of two parameters, one affecting the growth state and the other asymptotic behavior. Here, the mathematical relationships between the Koya-Goshu model and the widely used growth models such as Brody, Von Bertalanffy, Richards, Weibull, Monomolecular, Mitscherlich, Gompertz, Classical Logistic, Generalized Logistic Function and the special situation of the Logistic Function are examined in detail and shown in a flowchart. This growth model is so flexible that it has the capacity to produce new useful models that have never been used. In addition, the mentioned growth models above are considered and it is clearly stated that each one has a solution of the speed-state differential equation describing the biological growth. Relative growth rate functions and their growth are examined as solutions of the velocity-state equation. The relative growth function tr , the Integral Constant logC and the parameter B were created for the functions described above. Derivatives of the models are presented in detail considering non-mathematics researchers working in the fields of biology and unavailability of these derivatives in literature.