Entropy in Chaotic Feedback Loops

Non-linear dynamical systems can exhibit sensitive dependence on initial conditions. This research explores Lyapunov exponent estimation for quantifying information entropy across nested feedback loops.

Motivation

In control theory, nested feedback loops are essential for stability. However, beyond critical gain values, these loops enter chaotic regimes where behaviour becomes fundamentally unpredictable.

Method

We compute the maximal Lyapunov exponent using the Benettin algorithm across a parameter sweep, mapping the boundary between ordered and chaotic regimes.

Findings

The phase boundary exhibits fractal structure, suggesting that even small perturbations to system parameters can push a stable controller into chaos.