TRANSITION FOR FINITE GLOBALLY COUPLED OSCILLATORS DRIVEN BY ADDITIVE AND MULTIPLICATIVE NOISES

We study an ensemble of N globally coupled oscillators driven simultaneously by additive and multiplicative noises. By numerical simulation we find that for this model there is the same transition in the dynamics of the mean field when the coupling constant is increased as the one proposed by Pikovsky et al. (Z.Phys. B95(1994), 541). The effect of the multiplicative noises on the transition is that when the multiplicative noise strength D₁ is small, the effect of the multiplicative noises on the transition is feeble; but with the increase of D₁ the transition is strongly influenced near a special value D′₁ of D₁; then with the increase of D₁ when the value of D₁ is larger than a critical value D₁⁰, the transition disappears. By some approximation we obtain the critical value D₍₁₎⁰ of D₁.