Ring Oscillators Under Nonlinear Coupling: Bifurcation and Chaos

Abstract

The dynamics of two non-linearly coupled ring oscillators are examined in this study. Each ring oscillator consists of three-stage inverters, coupled through a resistor and diode. The system is mathematically modeled by non-linear differential equations. A numerical phase plane, bifurcation, and quantitative measures, like the Lyapunov exponent, confirm the transition from periodic to chaotic oscillation in a broad parameter zone. The system is implemented in a prototype hardware electronic circuit with bifurcation and chaos observed experimentally. This circuit can be used in practical applications such as cryptography and random number generation.