Logistic equation in continuous form:
$\frac{\mathrm{d} y}{\mathrm{d} t} = ry(1 - ay)$ (Autonomous Differential Equations and Population Dynamics, equation 6 in Boyce Diprima's book, eleventh Edition)
Considering a = 1:
$\frac{\mathrm{d} y}{\mathrm{d} t} = ry(1 - y)$
Logistic equation in discrete form:
$y_{n + 1} = ry_n(1-y_n)$ (Logistic map - Wikipedia )
How to prove, or how to obtain one model from another ? I mean, for example, how can I reach the discrete equation starting from continuous equation and prove that both are equivalents ?