We analyze a two-mode laser; described by rate equations, whose gain i
s periodically modulated. The nature of the response varies significan
tly with the modulation amplitude. We study both the small modulation
in which the pump parameter remains always above the lasing threshold
for the second mode, and the deep modulation in which the pump paramet
er is located during part of the,cycle between the single-mode and the
two-mode thresholds. Apart from the strong McCumber nonlinear resonan
ce at the relaxation oscillation frequency, we describe a rich variety
of nonlinear properties such as multistability among periodic and qua
si-periodic solutions, and small resonances in the vicinity of the sec
ond (and lower) internal frequency. We also identify domains that sugg
est the occurrence of the traditional routes to chaos.