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)

  1. f(x) = x^3/3 - x
  2. f(x) = x^3/3 + x
  3. f(x) = x^4/4 - x^2/2
  4. f(x) = x^4/4
  5. f(x) = x^4/4 + x^2/2
HW#9B: Draw response diagrams for these schemes,
  1. the fold: f_a(x) = x^3/3 + ax, with a in [-1,1]
  2. the cusp: f_(a,b)(x) = x^4/4 + ax^2/2 + bx, with a = -1, and b in [-2,2]
  3. the cusp, with a = +1, and b in [-2,2]
  4. describe the change in the cusp response diagram as a changes from -1 to +1
  5. draw the cusp bifurcation surface in 3D

Revised 27 Feb 2004 by RHA