How to nondimensionalize the equation $dN/dt=N[s - m(N - a)^2]$?
By Emily Wilson •
I have a differential equation for population growth, which is
$$dN/dt=N[s - m(N - a)^2]$$
How to nondimensionalize the equation so it can depends on a single dimensionless parameter $k= a(m/s)^{1/2}$?
$\endgroup$1 Answer
$\begingroup$Define $N(t)=a x $ and $\tau=s t$. Then the differential equation becomes
$$\frac{\mbox{d}x}{\mbox{d}\tau} = x [1-k^2 (x-1)^2]$$
where $k^2=m a^2/s$ as desired.
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