Synchronization and stochastization of an ensemble of self-oscillators by external noise

A theoretical investigation is made of the behavior of an emsemble of noninteracting self-oscillators under the effect of external delta-correlated pulse noise. A stochastic mapping is obtained which relates the amplitudes and phases between successive pulses. It is shown that, depending on the motion stability in the phase space, either a synchronization regime (where the phase and amplitudes of all the oscillators coincide) or a stochastization regime (where the phases are uncorrelated) arises; synchronization or stochastization is determined according to the Liapunov characteristic exponent. The transition from synchronization to stochastization is shown to occur as the noise intensity and the degree of oscillation nonisochronicity increase.