High resolution experimental parameter space of a chaotic circuit

TL;DR

This study provides a detailed experimental analysis of a chaotic circuit's parameter space, revealing both expected and novel features, and introduces a high-resolution potentiometer for better exploration of circuit behaviors.

Contribution

The paper introduces a new high-resolution potentiometer for experimental parameter variation and demonstrates its effectiveness in revealing complex behaviors in a chaotic circuit.

Findings

Identification of novel features in the chaotic and periodic regions.

Confirmation of exponential decrease in size of periodic regions with increasing period.

Observation that higher-period behaviors are unlikely due to shrinking periodic regions.

Abstract

We have obtained a high resolution parameter space of an experimental Chua's circuit and shown that the topology of the chaotic and periodic regions present not only expected features previously observed from high resolution numerical simulations of idealised Chua's circuit, but also novel unexpected features. Unmatched feedback resistances cause the formation of at least two competing spirals with consequent disrupted or malformed shrimps. We have also confirmed experimentally that the period-adding bifurcation route is formed by periodic regions whose size decrease exponentially with their period, and consequently, periodic behaviour with higher period is unlikely to be observed. The higher-resolution span of parameters was possible by the use of a newly designed potentiometer that could be potentially used in other electronic equipments to reveal hidden behaviours. To have such resistances we developed in series arrays of resistors short-circuited by relays as discrete potentiometers with 1024 steps, and resolutions of 0.100 $\Omega$ for $r_L$ in series with the inductor, and 0.200 $\Omega$ for R connecting the two capacitors.