Deriving five growth functions from bertalanffy function based on symmetry and complexity

Masataka Shimojo, Yutaka Nakano, Manabu Tobisa, Tao Shao

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

This study was designed to derive five growth functions from Bertalanffy function using symmetry and complexity of them by relating each function to its first and second derivatives. The results obtained were as follows. In equations constructed by relating functions to their derivatives, the left-hand sides were the same in form, but the right-hand sides showed differences from the symmetry essential to exponential function. These differences were related to complexity of functions approaching asymptotes. The asymptotic properties of five functions were shown by phenomena that the right-hand sides tended to zero as í tended to infinity. Six growth functions arranged by the complexity were Bertalanffy > Richards > Mitscherlich = logistic = Gompertz > basic growth. Despite different function forms, Mitscherlich, logistic and Gompertz functions were not distinguished each other from the viewpoint of complexity, a kind of symmetry existing at the base of them. Based on symmetry and complexity, five growth functions were derived from Bertalanffy function, a hierarchic structure of growth functions from Bertalanffy function on down.

Original languageEnglish
Pages (from-to)151-152
Number of pages2
JournalJournal of the Faculty of Agriculture, Kyushu University
Volume57
Issue number1
Publication statusPublished - Feb 1 2012

Fingerprint

hands
Growth

All Science Journal Classification (ASJC) codes

  • Biotechnology
  • Agronomy and Crop Science

Cite this

Deriving five growth functions from bertalanffy function based on symmetry and complexity. / Shimojo, Masataka; Nakano, Yutaka; Tobisa, Manabu; Shao, Tao.

In: Journal of the Faculty of Agriculture, Kyushu University, Vol. 57, No. 1, 01.02.2012, p. 151-152.

Research output: Contribution to journalArticle

@article{be9b77f4b8f54c9d8ef7f208c629cbfe,
title = "Deriving five growth functions from bertalanffy function based on symmetry and complexity",
abstract = "This study was designed to derive five growth functions from Bertalanffy function using symmetry and complexity of them by relating each function to its first and second derivatives. The results obtained were as follows. In equations constructed by relating functions to their derivatives, the left-hand sides were the same in form, but the right-hand sides showed differences from the symmetry essential to exponential function. These differences were related to complexity of functions approaching asymptotes. The asymptotic properties of five functions were shown by phenomena that the right-hand sides tended to zero as {\'i} tended to infinity. Six growth functions arranged by the complexity were Bertalanffy > Richards > Mitscherlich = logistic = Gompertz > basic growth. Despite different function forms, Mitscherlich, logistic and Gompertz functions were not distinguished each other from the viewpoint of complexity, a kind of symmetry existing at the base of them. Based on symmetry and complexity, five growth functions were derived from Bertalanffy function, a hierarchic structure of growth functions from Bertalanffy function on down.",
author = "Masataka Shimojo and Yutaka Nakano and Manabu Tobisa and Tao Shao",
year = "2012",
month = "2",
day = "1",
language = "English",
volume = "57",
pages = "151--152",
journal = "Journal of the Faculty of Agriculture, Kyushu University",
issn = "0023-6152",
publisher = "Faculty of Agriculture, Kyushu University",
number = "1",

}

TY - JOUR

T1 - Deriving five growth functions from bertalanffy function based on symmetry and complexity

AU - Shimojo, Masataka

AU - Nakano, Yutaka

AU - Tobisa, Manabu

AU - Shao, Tao

PY - 2012/2/1

Y1 - 2012/2/1

N2 - This study was designed to derive five growth functions from Bertalanffy function using symmetry and complexity of them by relating each function to its first and second derivatives. The results obtained were as follows. In equations constructed by relating functions to their derivatives, the left-hand sides were the same in form, but the right-hand sides showed differences from the symmetry essential to exponential function. These differences were related to complexity of functions approaching asymptotes. The asymptotic properties of five functions were shown by phenomena that the right-hand sides tended to zero as í tended to infinity. Six growth functions arranged by the complexity were Bertalanffy > Richards > Mitscherlich = logistic = Gompertz > basic growth. Despite different function forms, Mitscherlich, logistic and Gompertz functions were not distinguished each other from the viewpoint of complexity, a kind of symmetry existing at the base of them. Based on symmetry and complexity, five growth functions were derived from Bertalanffy function, a hierarchic structure of growth functions from Bertalanffy function on down.

AB - This study was designed to derive five growth functions from Bertalanffy function using symmetry and complexity of them by relating each function to its first and second derivatives. The results obtained were as follows. In equations constructed by relating functions to their derivatives, the left-hand sides were the same in form, but the right-hand sides showed differences from the symmetry essential to exponential function. These differences were related to complexity of functions approaching asymptotes. The asymptotic properties of five functions were shown by phenomena that the right-hand sides tended to zero as í tended to infinity. Six growth functions arranged by the complexity were Bertalanffy > Richards > Mitscherlich = logistic = Gompertz > basic growth. Despite different function forms, Mitscherlich, logistic and Gompertz functions were not distinguished each other from the viewpoint of complexity, a kind of symmetry existing at the base of them. Based on symmetry and complexity, five growth functions were derived from Bertalanffy function, a hierarchic structure of growth functions from Bertalanffy function on down.

UR - http://www.scopus.com/inward/record.url?scp=84858418054&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84858418054&partnerID=8YFLogxK

M3 - Article

VL - 57

SP - 151

EP - 152

JO - Journal of the Faculty of Agriculture, Kyushu University

JF - Journal of the Faculty of Agriculture, Kyushu University

SN - 0023-6152

IS - 1

ER -