| Summary: | 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 some previous results, some notes are given for a class of systems concerning focus quantities, center manifolds and Hopf bifurcations. The analysis of Hopf bifurcations on the center manifolds is carried out based on the computation of focus quantities and other analytical techniques. For each equilibrium, the structure of the bifurcation set is explored in depth. It is proved through the study of Bautin bifurcations that the system can have at most four small limit cycles (on the center manifolds) in two nests and this bound is sharp.
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