Hopf Bifurcations in a Watt Governor With a Spring

TL;DR

This paper analyzes complex bifurcation phenomena in a Watt governor with a spring, extending previous work to higher codimension Hopf bifurcations, and explores stability and coexistence of multiple attractors.

Contribution

It investigates higher codimension Hopf bifurcations in the Watt governor system, providing detailed bifurcation diagrams and stability analysis, which were not previously studied.

Findings

Identification of regions with coexisting attractors

Analysis of Lyapunov stability coefficients for bifurcations

Determination of bifurcation diagrams and orbit types

Abstract

This paper pursues the study carried out by the authors in "Stability and Hopf bifurcation in a hexagonal governor system", focusing on the codimension one Hopf bifurcations in the hexagonal Watt governor differential system. Here are studied the codimension two, three and four Hopf bifurcations and the pertinent Lyapunov stability coefficients and bifurcation diagrams, ilustrating the number, types and positions of bifurcating small amplitude periodic orbits, are determined. As a consequence it is found an open region in the parameter space where two attracting periodic orbits coexist with an attracting equilibrium point.