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UCSC Math 23a, Winter 2004
Exercizes for Catastrophe Theory
HW#9A1: Read pp. 1-5 of (Zeeman, 1976)
HW#9A2: Draw the graph of the potential function, f,
and the attractor-basin portrait for the gradient vfd,
v = grad (f)
- f(x) = x^3/3 - x
- f(x) = x^3/3 + x
- f(x) = x^4/4 - x^2/2
- f(x) = x^4/4
- f(x) = x^4/4 + x^2/2
HW#9B: Draw response diagrams for these schemes,
- the fold: f_a(x) = x^3/3 + ax, with a in [-1,1]
- the cusp: f_(a,b)(x) = x^4/4 + ax^2/2 + bx,
with a = -1, and b in [-2,2]
- the cusp, with a = +1, and b in [-2,2]
- describe the change in the cusp response diagram
as a changes from -1 to +1
- draw the cusp bifurcation surface in 3D
Revised 27 Feb 2004 by RHA
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