  The displacement of a viscous liquid by air in the narrow gap between two
parallel plates - a Hele-Shaw channel - is an exemplar of complex pattern
formation. Typically, bubbles or fingers of air propagate steadily at low
values of the driving parameter. However, as the driving parameter increases,
they can exhibit disordered pattern-forming dynamics. In this paper, we
demonstrate experimentally that a remote perturbation of the bubble's tip can
drive time-periodic bubble propagation: a fundamental building block of complex
unsteady dynamics. We exploit the propensity of a group of bubbles to
self-organise into a fixed spatial arrangement in a Hele-Shaw channel with a
centralised depth-reduction in order to apply a sustained perturbation to a
bubble's shape as it propagates. We find that the bubble with a perturbed shape
begins to oscillate after the system undergoes a supercritical Hopf bifurcation
upon variation of the tip perturbation and dimensionless flow rate. The
oscillation cycle features the splitting of the bubble's tip and advection of
the resulting finger-like protrusion along the bubble's length until it is
absorbed by the bubble's advancing rear. The restoral of the bubble's tip
follows naturally because the system is driven by a fixed flow rate and the
perturbed bubble is attracted to the weakly unstable, steadily propagating
state that is set by the ratio of imposed viscous and capillary forces. Our
results suggest a generic mechanism for time-periodic dynamics of propagating
curved fronts subject to a steady shape perturbation.
