Analysis and improvement of Boolean chaos robustness to noise

Abstract

Boolean chaos generated by autonomous Boolean networks has been successfully applied to random number generation, physical unclonable function, gene regulation and reservoir computing, because it can generate complex dynamics with very simple structure. Influences of noise on autonomous Boolean networks chaotic system in delay time parameter spaces are analyzed by simulation and experiments in this article. It is found that the influences of noise on Boolean chaotic system is two-sided. What is new is that noise may lead to chaos instability, i.e., the noise transforms the original chaotic outputs into periodic outputs, which means the Boolean chaos lacks robustness to noise. Then like other chaotic systems noise contributes to Boolean chaotic unpredictability. The physical origin of noise induced Boolean chaos instability is analyzed that noise may easily change delay time parameter no longer a chaotic parameter in discontinuous chaotic parameter spaces. In addition, simulation and experiments on FPGA show that the increase of the number of nonlinear elements of the chaotic system can improve the Boolean chaos robustness to noise. This research is significant to the design of autonomous Boolean networks.