On The Controlled Chaos of S-Iteration According to Lyapunov Exponent and Certain Control Mechanisms in Discrete Dynamical Systems

Abstract

In this paper, our aim is to establish the control mechanism of the iteration process defined as S-iteration in the literature. First of all, it is to determine the dynamics of a system with chaotic property under S- iteration. Afterward, we investigate the stability state of the chaotic sys-tem under this iteration with the parameters of the S-iteration. In addition, using the chaotic logistic system, we will illustrate the theoretical results in this example in the MATLAB program. Finally, we will examine the periodic state of the S-iteration and investigate the cases in which the pe-riodic behavior is stable or unstable of the S-iteration with the Lyapunov exponent.