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.