Stability analysis of discrete dynamical system using khan-iteration technique

In the latest disciplines of research, controlling of chaos became the most important topic of research in non-linear dynamical systems which have large number of applications in engineering and scientific areas. In this reference, our objective is to develop controlling system by using the Picard-Mann hybrid procedure known as Khan-iteration. The chaotic region occur in dynamical systems due to the inconsistent periodic and fixed orbits of the system. Hence, the irregular periodic and fixed states are stabilized using control mechanism. Moreover, some theoretical and experimental results are observed which are followed by examples and theorems. At last, we examined the unstable states of the K-system and stabilized them by using Lyapunov exponent.