Coefficient criterion for four-dimensional Hopf bifurcations: a complete mathematical characterization and applications to economic dynamics (Q1433614)

The goal of the paper is to present a complete mathematical characterization of a coefficient criterion for four-dimensional Hopf bifurcations in a system with continuous time and to apply the authors' criterion to some typical models of economic dynamics. They consider the two-region business cycle model by \textit{T. Puu} [Nonlinear economic dynamics. 4th ed., Springer-Verlag, Berlin (1997; Zbl 0931.91024)] and the dynamic optimization model by \textit{E. J. Dockner} and \textit{G. Feichtinger} [J. Economics 53, No. 1, 31--50 (1991; Zbl 0733.90022)]. These applications revealed that the authors' coefficient criterion is practical and quite useful in detecting the cyclic behaviour analytically.