Bifurcation analysis of the Watt governor system. (English) Zbl 1182.70038

Sotomayor, Jorge; Mello, Luis Fernando; de Carvalho Braga, Denis

Comput. Appl. Math. 26, No. 1, 19-44 (2007).

Summary: This paper pursues the study carried out by the authors in Stability and Hopf bifurcation in the Watt governor system J. Sotomayor, L. F. Mello and D. de Carvalho Braga [Commun. Appl. Nonlinear Anal. 13, No. 4, 1–17 (2006; Zbl 1119.70015)], focusing on the codimension one Hopf bifurcations in the centrifugal Watt governor differential system, as presented in L. S Pontryagin’s book “Ordinary Differential Equations” [Addison-Wesley Publishing Company Inc., Reading (1962)]. Here are studied the codimension two and three Hopf bifurcations and the pertinent Lyapunov stability coefficients and bifurcation diagrams, illustrating the number, types and positions of bifurcating small amplitude periodic orbits, are determined. As a consequence it is found a region in the space of parameters where an attracting periodic orbit coexists with an attracting equilibrium.

MSC:

70K50	Bifurcations and instability for nonlinear problems in mechanics
70K20	Stability for nonlinear problems in mechanics

Keywords:

centrifugal governor; Hopf bifurcations; periodic orbit

Citations:

Zbl 1119.70015