Activated escape of periodically modulated systems

Area of Science:

• Physics
• Nonlinear Dynamics
• Statistical Mechanics

Background:

• Understanding noise-induced escape from metastable states is crucial in various physical and chemical systems.
• Periodically modulated systems exhibit complex dynamics influenced by noise and modulation parameters.

Purpose of the Study:

• To determine the noise-induced escape rate from a metastable state in a periodically modulated overdamped system for arbitrary modulation amplitude.
• To analyze the behavior of the instantaneous and period-averaged escape rates and identify scaling laws.

Main Methods:

• Analytical calculation of the escape rate for a periodically modulated overdamped system.
• Investigation of the instantaneous escape rate's dependence on modulation amplitude.
• Analysis of the prefactor in the period-averaged escape rate near the bifurcation amplitude.

Main Results:

• The instantaneous escape rate exhibits peaks that transition from Gaussian to strongly asymmetric with varying modulation.
• The prefactor of the period-averaged escape rate shows non-monotonic dependence on modulation amplitude A.
• Three distinct scaling regimes (zeta = 1/4, -1, 1/2) were identified near the bifurcation amplitude A(c).

Conclusions:

• The study provides a comprehensive analysis of noise-induced escape in modulated systems.
• The identified scaling regimes offer insights into the critical behavior near bifurcation points.
• The findings are relevant for understanding escape dynamics in periodically driven nonlinear systems.