Chapter 16
Stochastic Resonance
The thirst for something other than what we have. . .to bring
something new, even if it is worse, some emotion, some sorrow;
when our sensibility, which happiness has silenced like an idle
harp, wants to resonate under some hand, even a rough one, and
even if it might be broken by it.
(Marcel Proust, Swann’s Way)
16.1 Basic Stochastic Resonance Model
In the previous chapter we modeled a “nose” that detects some odor. Let us model
in this chapter an “ear” with a limited range of amplitudes of acoustic signals that it
can detect. The threshold of audible amplitudes is arbitrarily set at 0.03. Let us
specify a harmonic signal whose amplitude (0.01) is too low to be heard.
HARMONIC ¼ SINWAVE :01; :1
ð
Þþ:01
ð16:1Þ
Additionally, there is noise in the system.
NOISE ¼ RANDOM 0; :02
ð
Þ
ð16:2Þ
With the addition of noise the peak apparent amplitude to the ear is doubled,
goes above the audio threshold and thus can be “heard”:
COMBINED SIGNAL ¼ HARMONIC þ NOISE
ð16:3Þ
A save-disabled version of STELLA and the computer models of this book are available at
www.iseesystems.com/modelingdynamicbiologicalsystems.
B. Hannon and M. Ruth, Modeling Dynamic Biological Systems,
Modeling Dynamic Systems, DOI 10.1007/978-3-319-05615-9_16,
© Springer International Publishing Switzerland 2014
137