Bifurcations in Regional Migration Dynamics

Baldwin et al. (2003) show that the famous tomahawk bifurcation, which is used by Fujita et al. (1999) to explain the formation of the core-periphery pattern, disappears when two regions have uneven agricultural populations. Thus, this type of bifurcations result from intrinsic model symmetry. We provide a general analysis by examining, along arbitrary smooth parameter paths in a high dimensional parameter space and, this class of bifurcations that have crossing equilibrium loci. We found that, in a parameter space satisfying a mild rank condition, generically in all parameter paths this class of bifurcations do not appear