A novel one-dimensional chaotic map with improved sine map dynamics

Abstract

These days, keeping information safe from people who should not have access to it is very important. Chaos maps are a critical component of encryption and security systems. The classical one-dimensional maps, such as logistic, sine, and tent, have many weaknesses. For example, these classical maps may exhibit chaotic behavior within the narrow range of the rate variable between 0 and 1and the small interval's rate variable. In recent years, several researchers have tried to overcome these problems. In this paper, we propose a new one-dimensional chaotic map that improves the sine map. We introduce an additional parameter and modify the mathematical structure to enhance the chaotic behavior and expand the interval's rate variable. We evaluate the effectiveness of our map using specific tests, including fixed points and stability analysis, Lyapunov exponent analysis, diagram bifurcation, sensitivity to initial conditions, the cobweb diagram, sample entropy and the 0-1 test.