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

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

Extra (not in the textbook) Simple equation: y=x 3 +ax y=x 3 -10x y=x 3 y=x x General form for cusp: V(a,b)=x 4 +ax 2 +bx

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

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

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

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

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

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

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

Report Due date: Friday, August 4 th 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