Extensive numerical study and circuitry implementation of the Watt governor model

TL;DR

This paper presents a comprehensive numerical analysis and an analog electronic circuit implementation of the Watt governor model, revealing complex bifurcation structures and validating results through experimental circuitry, bridging theory and practical application.

Contribution

It introduces an innovative analog computing approach to experimentally analyze the Watt governor model, uncovering hierarchical bifurcations and stable periodic structures.

Findings

Discovery of self-organized stable periodic structures in the model

Hierarchical organization and period-adding bifurcation cascade observed

Experimental validation shows strong agreement with numerical results

Abstract

In this work we carry out extensive numerical study of a Watt-centrifugal-governor system model, and we also implement an electronic circuit by analog computation to experimentally solve the model. Our numerical results show the existence of self-organized stable periodic structures (SPSs) on parameter-space of the largest Lyapunov exponent and isospikes of time series of the Watt governor system model. A peculiar hierarchical organization and period-adding bifurcation cascade of the SPSs are observed, and this self-organized cascade accumulates on a periodic boundary. It is also shown that the periods of these structures organize themselves obeying the solutions of Diophantine equations. In addition, an experimental setup is implemented by a circuitry analogy of mechanical systems using analog computing technique to characterize the robustness of our numerical results. After applying an active control of chaos in the experiment, the effect of intrinsic experimental noise was minimized such that, the experimental results are in astonishing well agreement with our numerical findings. We can also mention as another remarkable result, the application of analog computing technique to perform an experimental circuitry analysis in real mechanical problems.