C. N. Jensen, M. Golubitsky, and H. True
Symmetry, Generic Bifurcations, and Mode Interaction in Nonlinear Railway Dynamics
International Journal of Bifurcation and Chaos 9 No. 7 (1999). To appear.
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.