Fractional order logistic map; Numerical approach

In this paper the fractional order logistic map in the sense of Caputo's fractional differences is numerically approached. It is shown that the necessary iterations number to avoid transients must be of order of thousand, not of order of hundreds as commonly used in several works. Also, it is revealed an interesting phenomenon according to which for every initial condition it correspond a different bifurcation diagram. This phenomenon seems to appear also in other FO difference systems, fact which could represent an obstacle for the numerical analysis. A short Matlab code is used to obtain the results.