  In this article is shown that large systems endowing phase coexistence
display self-oscillations in presence of linear feedback between the control
and order parameters, where an Andronov-Hopf bifurcation takes over the phase
transition. This is simply illustrated through the mean field Landau theory
whose feedback dynamics turns out to be described by the Van der Pol equation
and it is then validated for the fully connected Ising model following heat
bath dynamics. Despite its simplicity, this theory accounts potentially for a
rich range of phenomena: here it is applied to describe in a stylized way i)
excess demand-price cycles due to strong herding in a simple agent-based market
model; ii) congestion waves in queueing networks triggered by users feedback to
delays in overloaded conditions; iii) metabolic network oscillations resulting
from cell growth control in a bistable phenotypic landscape.
