The calculation of rate coefficients is a discipline of nonlinear science of importance to much
of physics, chemistry, engineering, and biology. Fifty years after Kramers' seminal paper on …

This review provides a pedagogic and self-contained introduction to master equations and
to their representation by path integrals. Since the 1930s, master equations have served as …

The eikonal approximation (instanton technique) is applied to the problem of large
fluctuations of the number of species in spatially homogeneous chemical reactions with the …

We outline the historical development of stochastic resonance (SR), a phenomenon in which
the signal and/or the signal-to-noise ratio in a nonlinear system increase with increasing …

The design of analogue electronic experiments to investigate phenomena in nonlinear
dynamics, especially stochastic phenomena, is described in practical terms. The advantages …

A prehistory problem is formulated for large occasional fluctuations in noise-driven systems.
It has been studied theoretically and experimentally, thereby illuminating the concept of …

We present analytic results for the current in a system moving in an arbitrary periodic
potential and driven by weak Gaussian noise with an arbitrary power spectrum which are …

The quasistationary distribution and the transition probabilities for systems driven by weak
noise are analyzed to logarithmic accuracy. The problem is reduced to the boundary-value …

In the weak noise limit (D→ 0), the escape rate over a one-dimensional potential barrier is
Γ∼ exp (− SD). Here S is calculated exactly by identifying appropriate instanton solutions in …

We evaluate the steady-state distribution and escape rate for an active Ornstein–Uhlenbeck
particle (AOUP) using methods from the theory of large deviations. The calculation is carried …