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

Year 2020, Volume: 10 Issue: 4, 2860 - 2871, 15.12.2020

Mehmet Korkmaz

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

Abstract

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.

Keywords

Hyperbolic Logarithmic Growth Models Monomolecular Logistic Gompertz

References

  • 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).

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

Year 2020, Volume: 10 Issue: 4, 2860 - 2871, 15.12.2020

Mehmet Korkmaz

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

Abstract

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.

Keywords

Hyperbolic Logarithmic Growth Models Monomolecular Logistic Gompertz

References

  • 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).
There are 8 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Matematik / Mathematics
Authors

Mehmet Korkmaz 0000-0002-7488-0552

Publication Date December 15, 2020
Submission Date March 9, 2020
Acceptance Date June 7, 2020
Published in Issue Year 2020 Volume: 10 Issue: 4

Cite

APA Korkmaz, M. (2020). A Study over the Hyperbolic and Logarithmic Monomolecular, Logistic and Gompertz Growth Models. Journal of the Institute of Science and Technology, 10(4), 2860-2871. https://doi.org/10.21597/jist.701238
AMA Korkmaz M. A Study over the Hyperbolic and Logarithmic Monomolecular, Logistic and Gompertz Growth Models. J. Inst. Sci. and Tech. December 2020;10(4):2860-2871. doi:10.21597/jist.701238
Chicago Korkmaz, Mehmet. “A Study over the Hyperbolic and Logarithmic Monomolecular, Logistic and Gompertz Growth Models”. Journal of the Institute of Science and Technology 10, no. 4 (December 2020): 2860-71. https://doi.org/10.21597/jist.701238.
EndNote Korkmaz M (December 1, 2020) A Study over the Hyperbolic and Logarithmic Monomolecular, Logistic and Gompertz Growth Models. Journal of the Institute of Science and Technology 10 4 2860–2871.
IEEE M. Korkmaz, “A Study over the Hyperbolic and Logarithmic Monomolecular, Logistic and Gompertz Growth Models”, J. Inst. Sci. and Tech., vol. 10, no. 4, pp. 2860–2871, 2020, doi: 10.21597/jist.701238.
ISNAD Korkmaz, Mehmet. “A Study over the Hyperbolic and Logarithmic Monomolecular, Logistic and Gompertz Growth Models”. Journal of the Institute of Science and Technology 10/4 (December 2020), 2860-2871. https://doi.org/10.21597/jist.701238.
JAMA Korkmaz M. A Study over the Hyperbolic and Logarithmic Monomolecular, Logistic and Gompertz Growth Models. J. Inst. Sci. and Tech. 2020;10:2860–2871.
MLA Korkmaz, Mehmet. “A Study over the Hyperbolic and Logarithmic Monomolecular, Logistic and Gompertz Growth Models”. Journal of the Institute of Science and Technology, vol. 10, no. 4, 2020, pp. 2860-71, doi:10.21597/jist.701238.
Vancouver Korkmaz M. A Study over the Hyperbolic and Logarithmic Monomolecular, Logistic and Gompertz Growth Models. J. Inst. Sci. and Tech. 2020;10(4):2860-71.