Applications of symbolic dynamics in counteracting the dynamical degradation of digital chaos

Chaotic systems which are realized on the finite precision devices suffer from dynamical degradation. In the literature, there does not seem to be good basis for designing schemes to reduce its negative influence on digital chaotic systems. Meanwhile, symbolic dynamics is often used to study the behaviors of complicated dynamical systems. In this paper, a new mechanism based on symbolic dynamics is proposed for designing effective schemes, in order to counteract the dynamical degradation of digital chaotic systems. A concrete scheme with hybrid structure is discussed to show significance of the mechanism. Symbolic dynamics are used to rigorously prove that a class of chaos-based digital systems can be perturbed to be chaotic again by a continuous chaotic system. Numerical experiments demonstrate that this scheme can recover the dynamical properties of original system, which is different from the existing remedies.