A 4 MHz Chaotic Oscillator Based on a Jerk System

Abstract

Chaotic oscillators have a wide range of possible applications including random number generation (RNG), a stimulation source for characterization of MEMS devices, spread spectrum communications, and audio range and RF noise sources. Some distinct characteristics of chaotic systems include topological mixing, determinism, long-term aperiodic behavior, sensitivity to initial conditions, as well as a spread spectrum response. In particular, the aperiodic behavior and sensitivity to initial conditions make chaotic oscillators an ideal candidate for RNG. In practice, one of the more important aspects of a RNG is the speed at which data/bits can be generated. In electronics, as the frequency of operation increases, so do the design restrictions and challenges. In addition, many of these chaotic systems are based on nonlinearities or complex math functions that are difficult to implement in electronic circuitry. Through careful selection of the system’s structure, complex behavior can be achieved in electronic circuitry with minimized component count, footprint and power consumption. Additionally, this concept reduces the design complexity compared to traditional techniques, and the jerk chaos architecture can aid in increasing the fundamental frequency by minimizing feedback paths in the chaotic oscillator. Presented in this work is a printed circuit board electronic implementation of a 4 MHz chaotic jerk system that exhibits complex, rich dynamics using very simple electronic circuits.