Box-models are important for qualitative description of thermohaline circulation. Their bifurcation analysis helps to understand possible mechanisms for the loss of stability. So far, bifurcations in box-models have been studied numerically, except for the saddle-node bifurcation in the Stommel type models. We consider a box model with turbulent fluxes. We prove that a rapid growth of the transfer function can lead to existence of a limit cyle. This limit cycle collapses to a steady state as the transfer function approaches the step function.
This talk is based on the team preprint with N.B. Melnikov:

A.A. Davydov, N.B. Melnikov. Existence of selfsustained oscillations in an acean circulation box model with turbulent fluxes. IIASA, IR-06-049.