Dynamical behavior of q-deformed logistic map in superior orbit

In this paper, we study the q-deformed logistic map in Mann orbit (superior orbit) which is a two-step fixed point iterative algorithm. The main aim of this paper is to investigate the whole dynamical behavior of the proposed map through various techniques such as fixed point and stability approach, timeseries analysis, bifurcation plot, Lyapunov exponent and cobweb diagram. We notice that the chaotic behavior of q-deformed logistic map can be controlled by choosing control parameters carefully. The convergence and stability range of the map can be increased substantially. Moreover, with the help of bifurcation diagrams, we prove that the stability performance of this map is larger than that of existing other one dimensional chaotic maps. This map may have better applications than that of classical logistic map in various situations as its stability performance is larger.