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In this work we carry out extensive numerical study of aWatt-centrifugal-governor system model, and we also implement an electroniccircuit by analog computation to experimentally solve the model. Our numericalresults show the existence of self-organized stable periodic structures (SPSs)on parameter-space of the largest Lyapunov exponent and isospikes of timeseries of the Watt governor system model. A peculiar hierarchical organizationand period-adding bifurcation cascade of the SPSs are observed, and thisself-organized cascade accumulates on a periodic boundary. It is also shownthat the periods of these structures organize themselves obeying the solutionsof Diophantine equations. In addition, an experimental setup is implemented bya circuitry analogy of mechanical systems using analog computing technique tocharacterize the robustness of our numerical results. After applying an activecontrol of chaos in the experiment, the effect of intrinsic experimental noisewas minimized such that, the experimental results are in astonishing wellagreement with our numerical findings. We can also mention as anotherremarkable result, the application of analog computing technique to perform anexperimental circuitry analysis in real mechanical problems.

Extensive numerical study and circuitry implementation of the Watt governor model