Stability and Hopf bifurcation in an hexagonal governor system

Bifurcation analysis of the Watt governor system

“…In the Section 4 we will analyze the stability of P 0 as ε c = 2 α β 3/2 . The change in the stability at the equilibrium P 0 as the parameters cross the critical surface produces a Hopf bifurcation in the WGS, whose analysis has been carried out by [1], [5] and, in a more general setting, by [14]. From (4), ε represents the friction coeffi cient of the system.…”

“…with G jk ∈ C. Solving for the vectors h i j the system of linear equations defi ned by the coeffi cients of the quadratic terms of (22), taking into account the coeffi cients of F in the expressions (13) and (14), one has…”

“…This paper pursues the study carried out by the authors in Stability and Hopf bifurcation in the Watt governor system [14], focusing on the codimension one Hopf bifurcations in the centrifugal Watt governor differential system, as presented in Pontryagin's book Ordinary Differential Equations, [13]. Here are studied the codimension two and three Hopf bifurcations and the pertinent Lyapunov stability coeffi cients and bifurcation diagrams, illustrating the number, types and positions of bifurcating small amplitude periodic orbits, are determined.…”

Bifurcation analysis of the Watt governor system

“…In the Section 4 we will analyze the stability of P 0 as ε c = 2 α β 3/2 . The change in the stability at the equilibrium P 0 as the parameters cross the critical surface produces a Hopf bifurcation in the WGS, whose analysis has been carried out by [1], [5] and, in a more general setting, by [14].…”

“…See also [10,14]. This paper starts reviewing the stability analysis due to Maxwell and Vyshnegradskii, which accounts for the characterization, in the space of parameters, of the structural as well as Lyapunov stability of the equilibrium of the Watt Centrifugal Governor System, WGS.…”