A Study over the Hyperbolic and Logarithmic Monomolecular, Logistic and Gompertz Growth Models

Yıl 2020, Cilt: 10 Sayı: 4, 2860 - 2871, 15.12.2020

Mehmet Korkmaz

https://doi.org/10.21597/jist.701238

Öz

In this study in addition to classical monomolecular, logistic and Gompertz models, their hyperbolic and logarithmic growth models were found. After that it is searched the effect of these hyperbolic and logarithmic growth models on the choice of appropriate growth model by using two separate data sets. For this purpose, classical monomolecular, logistic and Gompertz growth models and their hyperbolic and logarithmic growth models are compared with some model selection criteria such as coefficient of determination, error sum of squares. For two data sets it is found that the results of these hyperbolic and logarithmic growth models are better than the results of these growth models. Thus, it is considered that these hyperbolic and logarithmic growth models can be used in addition to these growth models. Even the results of these hyperbolic and logarithmic growth models were found the same for both data sets. In addition, some other hyperbolic and logarithmic growth models can be investigated for getting the best model choice.

Anahtar Kelimeler

Hyperbolic, Logarithmic, Growth Models, Monomolecular, Logistic, Gompertz

Kaynakça

• Brody S, 1945. Bioenergetics and Growth, Rheinhold Publishing, New York.
• Burkhart HE, Strub MR, 1974. A model for simulation or planted loblolly pine stands. In growth models for tree and stand simulation. Edited by J. Fries. Royal College of Forestry, Stockholm, Sweden. Pp.128-135. Model of forest growth. J. Ecol.60:849-873.
• Kansal AR, Torquato S, Harsh GR, 2000. Simulated brain tumor growth dynamics using a three dimentional cellular automaton. J Theor Biol, 203:367-382.
• Kara C, Alp A, Can F, 2011. Growth and Reproductive Properties of Flathead Trout (Salmo platycephalus Bhenke, 1968) Population from Zamanti Stream, Seyhan River, Turkey. Turkish Journal of Fisheries and Aquatic Sciences, 11: 367-375.
• Oyamakin, SO, Chukwu AU, 2015. On the Hyperbolic Monomolecular Growth Model in Height/Diameter Growth of PINES, Journal of Applied Mathematics, Statistics and Informatics, 11(1):5-17.
• Ricker, WE, 1979. Growth rates and models, Fish Physiol, 8: 677-743.
• Winsor, CP, 1932. The Gompertz curve as a growth curve, Proc. Natl. Acad. Sci.,18(1): 1-8.
• Yıldızbakan A, 2005. Analysis on mathematical models of tree growth and comparison of these models, MSc Thesis, Institute of Natural and Applied Sciences, University of Cukurova, Turkey, (in Turkish, with abstract in English).