This paper is concerned with the qualitative analysis of a financial system.We focus our interest on the stability and cyclicity of the equilibria. Based on someprevious results, some notes are given for a class of systems concerning focus quantities, center manifolds and Hopf bifurcations. The analysis of Hopf bifurcations onthe center manifolds is carried out based on the computation of focus quantities andother analytical techniques. For each equilibrium, the structure of the bifurcation set isexplored in depth. It is proved through the study of Bautin bifurcations that the systemcan have at most four small limit cycles (on the center manifolds) in two nests and thisbound is sharp.
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