We investigate Cooperrider's complex bogie, a mathematical model of a railway bogie running on an ideal straight track. The speed of the bogie v is the control parameter. Taking symmetry into account, we find that the generic bifurcations from a symmetric periodic solution of the model are Hopf bifurcations for maps (or Neimark bifurcations), saddle-node bifurcations, and pitchfork bifurcations. The last ones are symmetry-breaking bifurcations. By variation of an additional parameter, bifurcations of higher degeneracy are possible. In particular, we consider mode interactions near a degenerate bifurcation. The bifurcation analysis and path-finding are done numerically.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.