Generalized Two-Parameter Equation of Growth

Miljenko Marušić, Željko Bajzer

Research output: Contribution to journalArticlepeer-review

35 Scopus citations


We considered the general growth equation y′ = ayα + byβ that encompasses the well-known growth equations by Bertalanffy and Verhulst-Pearl (logistic) as special cases. The solutions of this equation for some values of α and/or β can be found in the literature. Here we present the general solution for any real α and β and discuss its behavior. We found that the generalized Gompertz growth equation y′ = ayα + byα ln y and its solution could be considered a limiting case of the general growth equation and its solution, respectively. Thus, all three classical growth models (Bertalanffy, logistic, and Gompertz) are nested within the general model. This nesting relationship makes it possible to compare statistically the applicability of models to data.

Original languageEnglish (US)
Article number71361
Pages (from-to)446-462
Number of pages17
JournalJournal of Mathematical Analysis and Applications
Issue number2
StatePublished - Nov 15 1993

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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