Abstract. 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. As a consequence it is found a region in the space of parameters where an attracting periodic orbit coexists with an attracting equilibrium.Mathematical subject classification: 70K50, 70K20.

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In this paper, we study the existence of limit cycles for piecewise linear differential systems with two zones in the plane. More precisely, we prove the existence of piecewise linear differential systems with two zones in the plane with four, five, six and seven limit cycles. From our results we conjecture the existence of piecewise linear differential systems with two zones in the plane having exactly n limit cycles for all n ∈ ℕ.

Abstract. 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. As a consequence it is found a region in the space of parameters where an attracting periodic orbit coexists with an attracting equilibrium.Mathematical subject classification: 70K50, 70K20.

In this paper we study the local codimension one, two and three Hopf bifurcations which occur in the classical Chua's differential equations with cubic nonlinearity. A detailed analytical description of the regions in the parameter space for which multiple small periodic solutions bifurcate from the equilibria of the system is obtained. As a consequence, a complete answer for the challenge proposed in [Moiola & Chua, 1999] is provided.