  We propose an exactly solvable quasi-classical model of a spaser. The gain
medium is described in terms of the nonlinear permittivity with negative
losses. The model demonstrates the main features of a spaser: a
self-oscillating state (spasing) arising without an external driving field if
the pumping exceeds some threshold value, synchronization of a spaser by an
external field within the Arnold tongue, and the possibility of compensating
for Joule losses when the pumping is below threshold. Similar to the common
laser, a transition to the spasing regime takes a form of the Hopf bifurcation.
