Theoretical design and circuit implementation of novel digital chaotic systems via hybrid control

Abstract

Abstract Chaos is a paradigm shift of all science, which provides a collection of concepts and methods to analyze a novel behavior that can arise in a wide range of disciplines. However, most of researches in simulations and applications of chaos are performed on finite-state automata, which inevitably causes chaos to collapse. Here we present a hybrid model by controlling digital system with continuous chaotic system to construct chaos on finite-state automata. A new concept and method named Generalized Symbolic Dynamics (GSD) is proposed to target the hybrid system. Based on GSD, a rigorous proof is given that the controlled digital system is chaotic in the sense of Devaney. Moreover, analog-digital hybrid circuit is built for the digital chaotic system. Finally, a simple pseudorandom number generator is designed as a proof of concept. Results show that the proposed generator has good performance for cryptography. Such digital chaotic systems, which are not subject to degradation, could pave the way for widespread applications of chaos.