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It should be noted that, for '0, the steady state A"0 loses its stability and the state AO0 becomes stable. 40) implies that the probability density of A is monotonically decreasing with increasing A for any values of '0 (see Fig. 13). The same result has also been obtained by numerical simulation. Hence, the appearance of a new stable state need not be accompanied by the appearance of a new maximum in the probability distribution. In the case when the intensity of additive noise is nonzero, the steady-state solution of Eq.

75) with f (t)" (t) are shown in Fig. 21(b) for the same values of the parameters as in Fig. 28. er very slightly in their form from those for the case of a harmonic variation of the contact rate. This is associated with the fact that the variation of the contact rate only induces the phase transition, whereas the shape of the induced oscillations is mainly determined by intrinsic properties of the system, manifesting themselves in the shape of free oscillations as well. The evolution of the oscillation power spectra in the case of a periodic variation of the contact rate is illustrated in Fig.

Noise-induced phase transitions in nonlinear oscillators In recent years the problem of nonequilibrium noise-induced phase transitions has attracted considerable attention from many scientists. These transitions are characterized by a qualitative change of the state of a system as the intensity of noise acting upon it increases. This change can manifest itself in the appearance of new extrema in the probability distribution for the system variables or disappearance of old ones [2,89], in either stabilization or destabilization of system equilibrium states [1,9], in the occurrence of so-called mean "eld [4}7], in the excitation of oscillations [1,8,9,11,10], in the appearance of supernarrow spectral peaks close to the transition [90,91], and other marked changes in behaviour.

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Physics Reports vol.323

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