Theoretical design of controlled digitized chaotic systems with periodic orbit of upper limit length in digital circuit

Abstract

When chaotic systems are realized in digital circuit, it will collapse in finite fields eventually and show complex periodic behavior. In the literature, there do not seem to be good bases for designing schemes to reduce its negative influence on digitized chaotic systems in digital circuit. In this paper, the influence of digital circuit on chaotic system is studied, and an approach based on the introduction of control terms is discussed to improve the periodic orbits of digitized chaotic systems. The approach is illustrated using the digitized chaotic Logistic map as a typical example. It is proved that the periodic orbits of digitized Logistic map can be well controlled, and the length of periodic orbit can reach the upper limit. Furthermore, the simplest nonlinear dynamical system based on digitized Logistic map in digital circuit is proposed, in which the length of periodic orbit also reaches the upper limit.