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Bi- and multi-logistic curves

As it turns out, many growth and diffusion processes are actually made up of several subprocesses. First, let us consider the case of a system which experiences growth in two discrete growth phases. Then, we will extend this to an arbitrary number of phases.

Systems with two growth phases follow what we call the ``Bi-logistic'' model [12]. In this model, growth is the sum of two discrete ``wavelets'' , each of which is a three-parameter logistic:

 
N(t) = N1(t) + N2(t), (5)

where

\begin{eqnarray*}N_1(t)= \frac{\kappa_1}{1 + \text{exp} \left[ {-\frac{\ln(81)}{...
...t{exp} \left[ {-\frac{\ln(81)}{\Delta t_2}}(t -t_{m2}) \right] }
\end{eqnarray*}


Naturally, we can examine system-level behavior (i.e., N(t)), or we can decompose the model and examine the behavior of the discrete components (either N1(t) or N2(t)). In fact, we can plot N1(t) and N2(t) on the same axes, and moreover we can compare two disparate wavelets by normalizing them with the Fisher-Pry transform.



Perrin S Meyer
1998-07-14