Chaotic solutions and global indeterminacy in a resource optimal model

The paper investigates the dynamical properties of a resource optimal system derived by Wirl (2004) and Bella (2010). To this end, we determine the whole set of conditions which lead to global indeterminacy and, eventually, chaotic behavior outside the small neighborhood of the Balance Growth Path (see, for example, Mattana et al., 2009, Nishimura and Shigoka, 2006, Venturi, 2014). As the parameters of the model are varied, the model exhibits a rich spectrum of dynamic behavior, namely from a stable equilibrium to a Hopf limit-cycle, either super-critical or sub-critical (see Mattana and Venturi 1999, Neri and Venturi 2007). Here, we focus on a parameter region of local determinacy. We show the possibility of global indeterminacy and chaos in its subset. It might be impossible to characterize the system for a full set of parameter spaces, and the boundary of a chaotic region. We describe the "routes to chaos", and a bifurcation diagram, where one could see how a change in some parameters can lead to a series of bifurcations: the emergence of a saddle-focus, of a homoclinic orbit, and chaos.