Analytical Solution of the Logistic Equation
Savely Rabinovich, Gregory Berkolaiko, Sergey V. Buldyrev, Arkady Shekhter, Shlomo Havlin · International Journal of Bifurcation and Chaos · 1997
An analytical solution for the well-known quadratic recursion, also known as the logistic map, is presented. Our derivation makes use of the analogy between this equation and Galton–Watson processes. The latter can be treated in a linear way using the transfer matrix technique. The solution is represented as a power of an appropriate transfer matrix.