Existence of Periodic and Chaotic Solutions in non Linear Economic-Financial Models

Techniques from dynamical systems, specifically from bifurcation theory, are used to investigate the occurrence of cycle and chaotic solutions in endogenous growth models with externality. In particularly, we consider a general class of endogenous growth models as formalized by Mulligan and Sala-i-Martin (1993), reducible in the form of a non linear three-dimensional system. The Lucas and the Romer model can be considered as particular examples of this general class. By equilibrium analysis around the steady state, we show that when an externality factor is included in these models, we can found a regions in the parameters space where we get indeterminacy (Benabib and Perli 2001), cycles (Mattana P. and Venturi B. 1999, Mattana 2005) and chaotic solutions (Bella G.,, Mattana P.,, Venturi B. 2012). It is found that chaotic behavior will be exhibited in the neighborhood of parameter space of economic models where certain homoclinic orbits occur. A global criterion is given to understand complicate phenomena related with endogenous growth models with externality. A numerical simulation of the solutions of some interesting models is presented