Physics 313: Lecture 8
Wednesday, 9/17/08
Comments to the Class
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You should be reading Chapter 4.
Read Appendix 1 on elementary bifurcations, review in
Strogatz if necessary.
From previous lecture
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Java demo illustrating collapse of initial wavevectors to ring then to points:
http://crossgroup.caltech.edu/Patterns/Demo4_1.html
http://crossgroup.caltech.edu/Patterns/Demo4_2.html
Today's topics:
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Application of Turing theory to Brusselator.
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Quantitative comparisons of theory with experiment
for reaction-diffusion systems.
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Nonlinear states.
Supplementary Reading: JD Murray
“Mathematical Biology, Second Edition”
Brusselator:
Model of Chemical Pattern Formation
A = [A] held constant as parameter
b = [B] held constant as parameter
monitor u1 = [X] and u2 = [Y]
What are appropriate boundary
conditions on concentrations?
Linear Stability of Brusselator Model
Brusselator Applets
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Brusselator in 2d periodic domain:
http://crossgroup.caltech.edu/Patterns/Demo4_5.html
Brusselator in 1d domain:
http://jcckit.sourceforge.net/examples.html
Phase space for zero-diffusion (fully mixed) dynamics
http://www.um.es/fem/EjsWiki/index.php/Main/ExamplesBrussel
ator