The operation of surface plasmon amplifier by stimulated emission of radiation (spaser) in the presence of external optical field is analyzed. The range of external field amplitude E and mismatch △ of the external field frequency and the spaser generation frequency (Arnold tongue) E > E_(synchr)(△) in which the spaser works at the external field frequency is determined. The analytical and numerical calculations at the given mismatch △ yield three ranges: E < E_(synchr)(△) (the spaser exhibits stochastic regime and point (△, E) is outside the Arnold tongue), E_(synchr)(△) < E < E_I(△) (transient range where the spaser polarization weakly depends on the field amplitude and is mainly determined by the pump level), and E> E_I (the spaser generation is suppressed and the spaser polarization is equal to the polarization of nanoparticle in the presence of external field).
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