  Many real systems comprised of a large number of interacting components, as
for instance neural networks , may exhibit collective periodic behavior even
though single components have no natural tendency to behave periodically.
Macroscopic oscillations are indeed one of the most common self-organized
behavior observed in living systems. In the present paper we study some
dynamical features of a two-population generalization of the mean field Ising
model with the scope of investigating simple mechanisms capable to generate
rhythm in large groups of interacting individuals. We show that the system may
undergo a transition from a disordered phase, where the magnetization of each
population fluctuates closely around zero, to a phase in which they both
display a macroscopic regular rhythm. In particular, there exists a region in
the parameter space where having two groups of spins with inter- and
intra-population interactions of different strengths suffices for the emergence
of a robust periodic behavior.
