Experimental Acquisition and Verification of Spectral Signatures of Dynamic Bifurcations

TL;DR

This paper presents an experimental framework using electronic circuits and data acquisition systems to capture spectral signatures of dynamical bifurcations, validating spectral bifurcation diagrams as a practical analysis tool.

Contribution

Develops an automated experimental method to obtain spectral bifurcation diagrams from real-time measurements of nonlinear systems.

Findings

Successfully captured spectral signatures of bifurcations experimentally

Strong qualitative agreement with numerical predictions despite noise

Established SBD as an effective experimental analysis tool

Abstract

Spectral bifurcation diagrams (SBDs) have recently emerged as an efficient tool for identifying dynamical transitions in nonlinear systems through frequency-domain analysis. Previous studies have been limited to numerical investigations, and the experimental realization of SBDs has remained unexplored. In this work, we develop an automated framework using analog electronic circuits and data acquisition (DAQ) systems to obtain SBDs from real-time measurements. The method enables controlled parameter variation and simultaneous acquisition of time-series data for spectral analysis. Using this approach, we experimentally capture characteristic spectral signatures of dynamical bifurcations, such as period-doubling, quasiperiodicity (two- and three-frequency), and torus length-doubling. The experimental results show strong qualitative agreement with the numerical predictions, despite noise and parameter mismatches. This study establishes SBD as an effective tool for the experimental analysis of nonlinear dynamical systems.