I-superior approach to study the stability of logistic map

Abstract

Verlhust logistic map f(x) = r x (1 − x) is a widely studied and applicable model in discrete dynamical system. Its behavior has been, extensively, studied in Picard orbit and recently studied in superior orbit. Rani et. al. [22] and [25] has shown that in superior orbit, logistic map is stable for larger values of r than that of Picard orbit. In this paper, we have attempted to make the map stable for further larger values of r via I-superior iterates.