  We study a generic model for the interaction of negative delayed feedback and
periodic forcing that was first introduced by Ghil et al. in the context of the
El Ni\~no Southern Oscillation (ENSO) climate system. This model takes the form
of a delay differential equation and has been shown in previous work to be
capable of producing complicated dynamics, which is organised by resonances
between the external forcing and dynamics induced by feedback. For certain
parameter values, we observe in simulations the sudden disappearance of
(two-frequency dynamics on) tori. This can be explained by the folding of
invariant tori and their associated resonance tongues. It is known that two
smooth tori cannot simply meet and merge; they must actually break up in
complicated bifurcation scenarios that are organised within so-called resonance
bubbles first studied by Chenciner.
  We identify and analyse such a Chenciner bubble in order to understand the
dynamics at folds of tori. We conduct a bifurcation analysis of the Chenciner
bubble by means of continuation software and dedicated simulations, whereby
some bifurcations involve tori and are detected in appropriate two-dimensional
projections associated with Poincar\'e sections. We find close agreement
between the observed bifurcation structure in the Chenciner bubble and a
previously suggested theoretical picture. As far as we are aware, this is the
first time the bifurcation structure associated with a Chenciner bubble has
been analysed in a delay differential equation and, in fact, for a flow rather
than an explicit map. Following our analysis, we briefly discuss the possible
role of folding tori and Chenciner bubbles in the context of tipping.
