1. Mathematical Models of Love & Happiness J. C. Sprott Department of Physics University of Wisconsin - Madison Presented to the Kiwanis Club of Downtown Madison in Madison, Wisconsin on June 3, 2002

2. Disclaimers It’s Strogatz’ fault This is not serious sociology I won’t get to the happiness part

3. The Mathematics R is Romeo’s love for Juliet (or hate if negative) J is Juliet’s love for Romeo dR/dt = aR + bJ a and b describe Romeo’s “Romantic Style”

5. What about Juliet? dJ/dt = cR + dJ She has her own style 4 parameters with 3 choices for each gives 81 different romantic pairings

7. Out of touch with their own feelings (continued) b > 0, c > 0 b < 0, c < 0 b > 0, c < 0 Two lovers Love fest (or war) Two nerds Unrequited love Nerd + lover Never-ending cycle War

8. With Self-Awareness and bc < 0 (nerd + lover) a + d < -2| bc | 1/2 a + d < 0 a + d > 0 Extremely cautious Rapid apathy Somewhat cautious Eventual apathy Overly eager Growing volatility (The only equilibrium is apathy)

13. Love Triangle Examples

15. Effect of Nonlinearities Replace ax with ax (1-| x |), etc. (logistic function) x ax ax (1 - | x |)

16. One Chaotic Solution of Nonlinear Love Triangle “ Strange attractor of love”