Local and global bifurcations in a model of the economic long wave

Abstract Combining mathematical analysis with simulations, we obtain a bifurcation diagram for a simple (two state variables) system dynamics model of the economic long wave. Previous linear analysis of the onset of oscillatory behavior (Hopf bifurcation) is extended to include nonlinear effects. It is shown that both sub‐ and supercritical Hopf bifurcation can occur. In the case of subcritical Hopf bifurcation, the system has two coexisting stable solutions, one stationary and one periodic, in a parameter interval below the bifurcation point. The importance of distinguishing between the two types of Hopf bifurcation is discussed. The model also exhibits homoclinic bifurcation to infinity for some parameter combinations: a limit cycle explodes and disappears. Finally, we discuss how the results may apply to other system dynamics models.