26 1. HEURISTICS

are equivalent to those describing overdamped motion of a particle in a periodi-

cally modulated double well potential, as described in the prototypical example of

Section 1.2.

The choice of examples we discussed in more detail is rather selective. The ef-

fects of stochastic resonance have been found in a big number of dynamical systems

in various further areas of the sciences, and studied by a variety of physical mea-

sures of quality of tuning. We just mention a big field of applications in microscopic

systems underlying the laws of quantum mechanics in which intrinsic quantum tun-

neling effects interfere with the interpretation of potential barrier tunneling that

can be seen as causing noise induced transitions in diffusion dynamics. See [108]

for a comprehensive survey. Stochastic resonance has further been observed in

passive optical bistable systems [30], in experiments with magnetoelastic ribbons

[100], in chemical systems [67], as well as in further biological ones [94, 60, 41].

Stochastic resonance may even be observed in more general systems in which the

role of periodic deterministic signals is taken by some other physical mechanisms

(see [108]).

1.5.7. Computational aspects of large deviation theory related to

stochastic resonance. Our theoretical approach aimed at explaining stochastic

resonance conceptually by means of space-time large deviations of weakly periodic

dynamical systems does not touch at all the field of numerical algorithms and sci-

entific computing for stochastic resonance related quantities which become very

important for applications especially in high dimensions. In the framework of the

classical Freidlin–Wentzell theory, first exit time estimates as well as large devia-

tions rates are analytically expressed by the quasi-potential (see Chapter 2) which

can be calculated more or less explicitly for gradient systems. To determine and

minimize the quasi-potential in high-dimensional scenarios is an analytically hardly

accessible task. In Vanden–Eijnden et al. [31, 53] practically relevant algorithms

with numerous applications for this task have been developed. They have been ap-

plied to various problems in different areas of application of stochastic resonance.