Study of a general growth model

Abstract

We discuss a general growth curve including several parameters, whose choice leads to a variety of models including the classical cases of Malthusian, Richards, Gompertz, Logistic and some their generalizations. The advantage is to obtain a single mathematically tractable equation from which the main characteristics of the considered curves can be deduced. We focus on the effects of the involved parameters through both analytical results and computational evaluations.

Figures (10)

• Figure 1: Scheme summarizing the results of Remark \ref{['remark1']}.
• Figure 2: Case 1: for several choices of the parameter $p$ with $1<p<1+\frac{1}{n}$, the general curve \ref{['sol2']} is compared with the Richard curve (black line), fixed $n=0.4$, $n=0.6$, $n=0.8$ and $n=1$. In the last case the Richard curve becomes the logistic curve.
• Figure 3: Case 1: for $p=1.5$ (on the left) and $p=1.9$ (on the right), the general curve \ref{['sol2']} is plotted for several choices of $n$ with $n<\frac{1}{1-p}$.
• Figure 4: Case 2: general curve in the case $p=1$ compared with the Logistic curve (black line), for several choices of $n$ ($<1$ on the left and $>1$ on the right).
• Figure 5: Case 3a: general curve for several choices of $n$ and for $m=\frac{1}{1-p}=2,4,6$ and $8$ (from left to right and from top to bottom)

Theorems & Definitions (2)

• Remark 2.1
• Remark 2.2