Coefficient criterion for four-dimensional Hopf bifurcations: a complete mathematical characterization and applications to economic dynamics

In this paper, we present a complete mathematical characterization of a coefficient criterion for four-dimensional Hopf bifurcations. Then, we apply our criterion to two typical models of economic dynamics. We consider the two-region business cycle model by Puu [Nonlinear economic dynamics, Springer-Verlag, Berlin, 1997] and the dynamic optimization model by Dockner and Feichtinger [J. Econom. 53 (1991) 31]. These applications reveal that our criterion is operative and useful in analyzing the qualitative properties of general four-dimensional dynamic economic models with continuous time.