Entropy of Chaotic Oscillations of Currents in the Chua Circuit and its HMM Analysis

TL;DR

This paper investigates the entropy of chaotic oscillations in the Chua circuit, analyzing how conductance influences oscillation patterns and applying Hidden Markov Models to characterize stable and unstable states.

Contribution

It introduces a novel analysis of entropy in chaotic currents of the Chua circuit and applies HMM to distinguish stable and unstable oscillation states.

Findings

Entropy is minimal in spiral steady states.

Maximum entropy occurs in double scroll chaotic states.

Eigenvector analysis of HMM transition matrices reveals stability characteristics.

Abstract

We study entropy of chaotic oscillation of electrical currents in the Chua's circuit controlled by triggering a pulse that brings the orbit that goes onto an unstable branch back to a stable branch. A numerical simulation of the voltage of the two capacitors and the current that flows on an inductor of the Chua's circuit reveals various oscillation patterns as the conductance that is connected between the two capacitors and directly connected to an inductor is varied. At small conductance, the Lissajous graph of the voltage of the two capacitors shows a spiral, while at high conductance a double scroll pattern appears. The entropy of the current that flows on the inductor is alocal minimum in the spiral state which is in the steady state, while it is maximum in the stable double scroll state. The stable double scroll samples are analyzed by using the Hidden Markov Model (HMM) and the eigenvectors of the transition matrix of long time series are found to be strictly positive but those of unstable short time series have negative components. We thus confirm maximum entropy production in the double scroll of the longest time series around the right fixed point, while the local minimum entropy production occurs in the spiral around the left fixed point.