Symmetry, generic bifurcations, and mode interaction in nonlinear railway dynamics

We investigate Cooperrider's complex bogie, a mathematical model of a railw ay bogie running on an ideal straight track. The speed of the bogie v is th e control parameter. Taking symmetry into account, we find that the generic bifurcations from a symmetric periodic solution of the model are Hopf bifu rcations for maps (or Neimark bifurcations), saddle-node bifurcations, and pitchfork bifurcations. The last ones are symmetry-breaking bifurcations. B y variation of an additional parameter, bifurcations of higher degeneracy a re possible. In particular, we consider mode interactions near a degenerate bifurcation. The bifurcation analysis and path-finding are done numericall y.