RS Flip-Flop Circuit Dynamics Revisited

TL;DR

This paper revisits the dynamics of logical RS flip-flop circuits using simple bilinear models, analyzing their behavior and perturbations to understand conditions leading to chaos and bifurcations.

Contribution

It introduces a minimal bilinear model for RS flip-flop circuits and analyzes how perturbations can induce chaotic regimes, connecting simple models with complex dynamical phenomena.

Findings

Minimal models exhibit expected properties but not chaos.

Perturbed models can show chaotic strange attractors.

Validation through comparison with traditional dynamical results.

Abstract

Logical RS flip-flop circuits are investigated once again in the context of discrete planar dynamical systems, but this time starting with simple bilinear (minimal) component models based on fundamental principles. The dynamics of the minimal model is described in detail, and shown to exhibit some of the expected properties, but not the chaotic regimes typically found in simulations of physical realizations of chaotic RS flip-flop circuits. Any physical realization of a chaotic logical circuit must necessarily involve small perturbations - usually with quite large or even nonexisting derivatives - and possibly some symmetry-breaking. Therefore, perturbed forms of the minimal model are also analyzed in considerable detail. It is proved that perturbed minimal models can exhibit chaotic regimes, sometimes associated with chaotic strange attractors, as well as some of the bifurcation features present in several more elaborate and less fundamentally grounded dynamical models that have been investigated in the recent literature. Validation of the approach developed is provided by some comparisons with (mainly simulated) dynamical results obtained from more traditional investigations.