Existence and implications of a pitchfork-Hopf bifurcation in a continuous-time two-sector growth model

Abstract This paper shows that the dynamics of Lucas (J Monet Econ, 22:3–42, 1988) endogenous growth model with flow externalities may give rise to a 2-torus, compact three-dimensional manifold enclosed by two-dimensional surface. The implications this result are relevant for many fields economic theory. It is first all clear if we choose initialize in basin attraction trapping region, continuum perfect foresight solutions be observed. A simple econometric exercise, linking physical-to-human capital ratio (state variable) 5-years forward variance rate an unbalanced sample 183 countries, seems provide empirical backing phenomenon. Other important consequences, from point view cycles theory, also scrutinized paper.