Activated Escape of Periodically Modulated Systems

The rate of noise-induced escape from a metastable state of a periodically modulated overdamped system is found for an arbitrary modulation amplitude $A$. The instantaneous escape rate displays peaks that vary with the modulation from Gaussian to strongly asymmetric. The prefactor $\nu$ in the period-averaged escape rate depends on $A$ nonmonotonically. Near the bifurcation amplitude $A_c$ it scales as $\nu \propto (A_c-A{)}^{\zeta }$. We identify three scaling regimes, with $\zeta =1/4$, $-1$, and $1/2$.

Figure 1

The prefactor $\nu$ in the average escape rate $\overline{W}$ (15). The results refer to a Brownian particle with $K(q,t)=q^2-1/4+A\cos ({\omega }_{F}t)$, ${\omega }_F=0.1$ and describe escape in the regime of strong synchronization, where $\nu \propto D^{1/2}$. The solid line for small $A$ shows the scaling $\nu \propto A^{-1/2}$ [10]. The solid line for small $A_c-A$ ($A_c\simeq 0.29$) shows the scaling (17). The dashed line shows the result of the numerical solution of Eq. (11). The squares and crosses show the results of Monte Carlo simulations for $R/D=5$ and $R/D=6$, respectively.