Mehrab Maps: One-Dimensional Piecewise Nonlinear Chaotic Maps

摘要: In this paper, we propose a new one-dimensional, two-segmental nonlinear map by combining tent, triangle and parabola curve functions. We call the proposed map, Mehrab since its return maps shape is similar to an altar (which it "Mehrab"). Definition properties of along with orbit diagrams, Lyapunov exponents, histograms are considered. To generate more uniform density function maps, two modified versions also defined. first modification (FMM), vertical symmetry transformation right used. Sensitivity initial condition total chaotic range FMM medium. Probability show uniformity. second (SMM) horizontal According diagrams sensitivity SMM large. This property gives region map. Its prove that probability uniform.