  We examine the gravitational collapse of a non-linear sigma model in
spherical symmetry. There exists a family of continuously self-similar
solutions parameterized by the coupling constant of the theory. These solutions
are calculated together with the critical exponents for black hole formation of
these collapse models. We also find that the sequence of solutions exhibits a
Hopf-type bifurcation as the continuously self-similar solutions become
unstable to perturbations away from self-similarity.
