From order to chaos: Bifurcations and parameter space organization in an analog Duffing-Holmes circuit

TL;DR

This paper experimentally explores the bifurcation structure and chaotic dynamics of an analog Duffing-Holmes oscillator, demonstrating the system's rich behaviors and validating the use of hardware for nonlinear dynamics studies.

Contribution

It provides a comprehensive experimental characterization of the Duffing-Holmes circuit's bifurcations and chaos, highlighting the effectiveness of analog hardware in nonlinear dynamics research.

Findings

Identified period-doubling routes to chaos.

Mapped multistability and intermittency regions.

Validated analog hardware as a reliable platform for nonlinear dynamics.

Abstract

We present an experimental study of the Duffing--Holmes oscillator with a double-well potential, implemented as an analog electronic circuit under periodic external forcing. By systematically varying the forcing amplitude and frequency, we characterize the full dynamical landscape of the system through bifurcation diagrams, Poincar\'e maps, and maximum Lyapunov exponent calculations. The observed phenomenology includes period-doubling routes to chaos, periodic windows with multistability, dynamical intermittency, and antiperiodic orbits in which the trajectory recovers the global symmetry of the double-well potential. These results are synthesized into a high-resolution two-dimensional phase diagram in parameter space. The close agreement between all experimental diagnostics validates the fidelity of the analog implementation and demonstrates that continuous-time hardware provides a powerful platform for the quantitative study of nonlinear dynamics, free from the discretization artifacts inherent to numerical simulation.