A novel parallel chaotic system with greatly improved Lyapunov exponent and chaotic range

Abstract

Lyapunov exponent (LE), chaotic range and complexity are the key considerations of a discrete chaotic system. A dynamic chaotic system with larger LE and wider parameter space will result in better statistical performance that can be used to generate pseudo random sequences and applied to encryption fields. At the same time, the combination of simple chaotic maps can generate more excellent chaotic behavior. This paper proposes a newly combined chaotic system called Parallel Chaotic System (PCS). Multiple simple chaotic maps are paralleled to construct the novel system. In this system, LE and chaotic range can be improved as much as possible by setting additional parameters. Compared with the existing models made up of same seed maps, PCS is able to get better chaotic behavior by means of a simple structure at the same time. Performance evaluation emphasizes that the chaotic maps generated by PCS are more unpredictable with better complexity.