  We analyze a bifurcation phenomenon associated with critical gravitational
collapse in a family of self-gravitating SU(2) $\sigma$-models. As the
dimensionless coupling constant decreases, the critical solution changes from
discretely self-similar (DSS) to continuously self-similar (CSS). Numerical
results provide evidence for a bifurcation which is analogous to a heteroclinic
loop bifurcation in dynamical systems, where two fixed points (CSS) collide
with a limit cycle (DSS) in phase space as the coupling constant tends to a
critical value.

General Relativity and Quantum Cosmology