I will discuss evidence for a homoclinic bifurcation sequence known
shilnikov phenomenon in a simple model of double-gyre ocean circulation.
This evidence, the first to our knowledge of a global bifurcation in an
ocean model, was obtained with a combination of time-delay embeddings of
time series and parametric imaging of power spectra. This evidence appears
to be obtainable in part because the ratio of two eigenvalues of the
homoclinic point is nearly critical, leading to the compression of strange
attractors around the homoclinic orbit in phase space. I will compare this
example with a similar case involving a bifurcation called a homoclinic
explosion, the real eigenvalue equivalent of the shilnikov phenomenon.