On the good modelling of certain growth processes (Q873917)

The author studies the relation between the continuous modelling (by a differential equation) of some growth processes and the corresponding discrete one. In order to show if the first one can be replaced by the second one without to commit a systematic error the author introduces the notion of ``step-stable'' functions \(f\) as the ones for which the quotient \((f(x+h)-f(x))/f'(x)h\) does not depend on \(x\), for all real \(x\) and \(h\neq 0\). It is shown that this is equivalent to state that \(f\) is of the form \(f(x)=mx +b\) or \(f(x)=ca^x+b\) (and satisfies a linear differential equation). The role of \(f\) is illustrated by some examples.