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Researchers should cite this work as follows:

• Tsoularis, A. (2023). 2001-Tsoularis-Analysis of logistic growth models. SIMIODE, QUBES Educational Resources. doi:10.25334/PJXG-CZ60

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Tsoularis, A.  2001. Analysis of logistic growth models. Research Letters in the Information and Mathematical Sciences. 2:23-46. 

See http://mro.massey.ac.nz/handle/10179/4341 . Accessed 27 March 2023.

Article Abstract:  A  variety of  growth  curves  have been  developed  to  model  both unpredated, intraspecific population dynamics and more  general  biological  growth. Most successful predictive models are shown to be based on extended forms of the classical Verhulst logistic growth equation.  We further review and compare several such models and calculate and investigate properties of interest for these. We also identify and detail several previously unreported associated limitations and restrictions. 

The paper presents an historical development of the logistic equation in its various forms, including Verhulst,  Pearl and Reed, Gompertz, Bertalanffy, Richards, and others. For each type of equation there is a section on analysis to include broad general behaviors and qualitative discussions.  The issues usually are around the variations and justifications as well as resulting analyses for different functional response terms, f(N), in the general logistic equation:

N’(t) = r N(t) f(N(t)).