A new experimental approach to study the stability of logistic map

Remarkably benign looking logistic transformations xn + 1 = rxn(1 − xn) for choosing x0 between 0 and 1 and 0 < r ⩽ 4 have found a celebrated place in chaos, fractals and discrete dynamics. The purpose of this paper is to enhance the capabilities of logistic map via superior iterations. Stability of logistic map has been studied by running computer programs. Logistic map is stable for 0 < r ⩽ 3.2 in Picard orbit. In superior orbit, we see that the range of stability of logistic map increases drastically. Also, chaotic behavior of logistic map disappears in certain cases.