Some Note about the Existence and Stability of Periodic solutions in non linear three-dimensional Economic Financial Models

In this paper we analyze the global structure of a tree-dimensional abstract continuous time stationary economic model that includes some determinates parameters. We use rigorous arguments to show as an equilibrium of the model could be destabilized into a stable cycle in the dynamic of R3 under the following two alternative assumptions. a) A steady state has three stable roots. b) A closed orbit has a two dimensional manifolds in which it is asymptotically stable, Next we apply this results to some related economic-financials models as a general new businesses IS-LM model as formulated by Neri and Venturi 2007, that undergo Hopf bifurcations for some parameters values. JEL classification: C62, E32 Keywords: deterministic cycles, Hoph bifurcations, stability of periodic orbits