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Unformatted text preview: 13 Experimental attractors In this brief lecture we show examples of strange attractors found in experi- ments. 13.1 Rayleigh-B´ enard convection BPV, Figure VI.25 Two dynamical variables, (Γ T ) and (Γ T ) ∗ , 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 (Γ T ) , (Γ ˙ T ) , and (Γ T ) ∗ . The Poincar´ e section in the plane (Γ T ) , (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). 13.2 Belousov-Zhabotinsky reaction See Strogatz, Section 8.3. The B-Z reaction is a particularly well studied chemical reaction that is of interest for • dynamics, because it is oscillatory; and • pattern formation and nonlinear waves....
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This note was uploaded on 02/24/2012 for the course MECHANICAL 12.006J taught by Professor Danielrothman during the Fall '06 term at MIT.
- Fall '06