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Catastrophe Theory

Mafuyu Kitahara English Theme8 2006-07-10 Summary of Chapter 15, Carver & Scheier (1998), On the Self-Regulation of Behavior, Cambridge Univ. Press. Catastrophe Theory. CUSP catastrophe. X: control parameter 1 Z: control parameter 2 Y: outcome As Z increases, X-Y becomes less linear.

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Catastrophe Theory

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  1. Mafuyu Kitahara English Theme8 2006-07-10 Summary of Chapter 15, Carver & Scheier (1998), On the Self-Regulation of Behavior, Cambridge Univ. Press. Catastrophe Theory

  2. CUSP catastrophe • X: control parameter 1 • Z: control parameter 2 • Y: outcome • As Z increases, X-Y becomes less linear

  3. Extra (not in the textbook) • Simple equation: y=x3+ax y=x3-10x y=x3 y=x3+0.5x • General form for cusp: V(a,b)=x4+ax2+bx

  4. Sensitive to initial cond • A slight change in x big difference in y when z becomes large • e.g. • x =You guys on 2005-04-01 • y =Grade • z =Time Some of you go over the top of the cliff, but others don't...

  5. Hysteresis • Difference of “where it comes from” • e.g., y=taste of cup noodle, x=temperature

  6. Variability • Between-subjects • Each dot = subjrect • Zero variability except around the cusp • Variability = either top or bottom surface • Within-subject • Repeated measure • Each dot = trial

  7. Applications (1): Perception • The initial perception is retained. • Start from Old...slow to change into Young • ... vice versa • Primacy effect • Bias • Prejudice

  8. Applications (2): Dating and Mating • x=attraction • z=social pressure • y=activity • Low social pressure • Attraction and dating quasi-linearly related • High social pressure • hysteresis

  9. Applications (3): Relationship • x=satisfaction • z=closeness • y=(de)commitment • Not close • Satisfaction and commitment quasi-linearly related • Close • hysteresis • About the same for... anything Groups Rumination vs. Action Expectancies Effort vs. disengagement

  10. Application (4) : Wortman & Brehm model • Different, but similar

  11. Report • Due date: Friday, August 4th • Required items: • Word-processor output • A4 paper, max 1000 words • School-of-Law coverpage • Theme: • Summary and commentary on any chapter(s) of the textbook or reference material

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