The Parallel Chaotification Map and Its Application

Abstract

A universal modular plus parallel (MPP) method is proposed to construct enhanced chaotic maps, including one-dimensional MPP chaotic map (1D-MPPCM) and high-dimensional MPPCM (HD-MPPCM). It is theoretically proved that 1D-MPPCM model can significantly increase the Lyapunov exponent (LE) and parameter range of seed chaotic maps. To further increase the system dimension, the HD-MPPCM model is established through the close-loop parallel coupling mechanism. Based on several typical seed chaotic maps, some new parallel chaotic maps are obtained by self-parallel and hybrid-parallel, and their dynamics are analyzed by phase diagram, LEs, permutation entropy (PE) complexity and statistic <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\chi^2$</tex-math> </inline-formula> . The simulation results show that the proposed maps have large maximum Lyapunov exponent (MLE), PE complexity, and uniform distribution. In particular, HD-MPPCMs have some interesting characteristics, such as full positive LEs, hyperchaotic behavior, global chaos, and full attractor distribution, which are the potential model for engineering applications. To further verify the practicability, the proposed maps are implemented on DSP platform, and applied to pseudo-random number generator (PRNG).