The hyperbolic sine chaotification model and its applications

Abstract

Some existing chaotic systems suffer from issues such as period windows, discontinuous parameter ranges, and dynamical degradation, which seriously limit their application. Therefore, designing high-performance anti-degradation chaotic systems is of great significance. In this paper, a novel hyperbolic sine chaotification model (HSCM) is proposed. It allows for the use of any chaotic maps or linear functions as the seed maps, and employs a closed-loop modulation coupling (CMC) method to extend it to high-dimensional (HD) chaotic maps. Theoretical and experimental results show that this model can effectively improve the Lyapunov exponent (LE) of the seed chaotic map and expand the parameter ranges. In addition, it can also resist the dynamical degradation under finite computational precision. Based on the HSCM, a novel eight-dimensional (8D) HSCM is designed, and implemented through field-programmable gate array (FPGA) in both serial and parallel modes, respectively. Furthermore, the novel chaotic maps are applied to pseudo-random sequence generator (PRNG) and image compression under finite computing precision. Experimental results indicate that the novel chaotification model has greatly broad application prospects.