On the Complex and Chaotic Dynamics of Standard Logistic Sine Square Map

Abstract

In this article, we set up a new nonlinear dynamical system which is derived by combining logistic map and sine square map in Mann orbit (a two step feedback process) for ameliorating the stability performance of chaotic system and name it Standard Logistic Sine Square Map (SLSSM). The purpose of this paper is to study the whole dynamical behavior of the proposed map (SLSSM) through various introduced aspects consisting fixed point and stability analysis, time series representation, bifurcation diagram and Lyapunov exponent. Moreover, we show that our map is significantly superior than existing other one dimensional maps. We investigate that the chaotic and complex behavior of SLSSM can be controlled by selecting control parameters carefully. Also, the range of convergence and stability can be made to increase drastically. This new system (SLSSM) might be used to achieve better results in cryptography and to study chaos synchronization.

Keywords

• standard logistic sine square map
• periodic and fixed points
• chaos
• time series plot
• bifurcation plot
• lyapunov exponent (le)
• primary 34h10, 37f45, 37b25
• secondary 37m10, 37c25