文档介绍：13 Experimental attractors
In this brief lecture we show examples of strange attractors found in experi­
ments.
Rayleigh-B´enard convection
BPV, Figure
Two dynamical variables, (ΓT ) and (ΓT )∗, represent time-dependent thermal
gradients measured measured by the refraction of light, inside the convecting
system.
A 3-D phase space is defined by the coordinates
(ΓT ), (Γ˙T ), and (ΓT )∗.
The Poincar´e section in the plane (ΓT ), (Γ˙T ) is obtained by strobing the
system at the dominant frequency of the fluctuations of one of the dynamical
variables.
Like the H´enon attractor, the points are arranged in a “complex but well-
defined structure”(BPV, p. 137).
Belousov-Zhabotinsky reaction
See Strogatz, Section .
The B-Z reaction is a particularly well studied chemical reaction that is of
interest for
dynamics, because it is oscillatory; and
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pattern formation and nonlinear waves.
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An example of the pattern formation is
Strogatz, Plate 1, Section
For us the dynamical aspects are of greater interest. This chemical reaction,
like many others, can be envisioned as a flux of reactants into a reactor, and
a flux of products out of the reactor:
reactants products
reactor
Nonlinearities arise from chemical reactions like
A + B C
∗
which yield terms like
dC
= AB
dt
The control parameter