Dynamics of Love IE604: System Dynamics Modeling and Analysis - PowerPoint PPT Presentation

Dynamics of Love IE604: System Dynamics Modeling and Analysis Jayendran Venkateswaran, IIT Bombay 14 th February Special

Classical Love Story ❤฀ ❤฀ ฀ ฀ • Let’s call them Romeo and Juliet • Romeo and Juliet are madly in love with each other. With each secret meeting, Romeo’s love for Juliet grows. Because he loves her, he does everything he can to impress her. Juliet is flattered by his attention and, in return, her love for Romeo also grows. Because Romeo senses that Juliet loves him, he allows his passion to soar. • What will happen to Romeo and Juliet’s love?

Model Romeo and Juliet’s Love • Let one lover’s love for the other be the stocks: • Romeo’s Love for Juliet • Juliet’s Love for Romeo • What will be the units for the stock? • “Love units” • Positive love units represent how much they like each other. • Negative love units represent how much they dislike each other • Zero love units represents they they are indifferent to each other.

Romeo Juliet Model Romeos Love for Juliet Change in Romeos Love Initial Love of Romeo for Juliet Romeos Reaction Juliets Love for Romeo Change in Juliets Love Initial Love of Juliet for Romeo Juliets Reaction • Romeo’s reaction to Juliet’s love is positive, and Juliet’s reaction to Romeo’s love is positive. • Parameter “Juliet’s Reaction” represents how Juliet reacts to Romeo’s love. • Say, each unit of Romeo’s love increases Juliet’s love by one unit each day. • Juliet’s Reaction = 1/day • Similar for “Romeo’s Reaction”

Run length = 12 days Simulating Romeo Juliet Model Time units days • Scenario 1: Initially, both Romeo and Juliet are attracted to each other  Initial value of Romeo’s Love is + 1 love units and Juliet’s love is also +1 units Trace the feedback loops

Run length = 12 days Simulating Romeo Juliet Model Time units days • Scenario 2: What will happen if initially Romeo loved Juliet twice as much as she loved him? Will Juliet’s love ever grow to equal Romeo’s love?  Initial value of Romeo’s Love is +2 love units and Juliet’s love is +1 units

Run length = 12 days Simulating Romeo Juliet Model Time units days • Scenario 3: Juliet is indifferent to Romeo. But Romeo find her attractive at first sight!  Initially, Juliet feel 0 love units for Romeo initially, while Romeo feels 1 love unit for Juliet

Run length = 12 days Simulating Romeo Juliet Model Time units days • Scenario 4 : Romeo’s family and Juliet’s family dislike each other. Suppose, influenced by their family, they both initially dislike each other  Initially, both feel -1 love units towards each other

Run length = 12 days Simulating Romeo Juliet Model Time units days • Scenario 5: Although Romeo is initially enchanted by Juliet, she feels an initial dislike for him.  initial value of Romeo’s love be +1 love unit and the initial value of Juliet’s love be -1 love unit.

Run length = 12 days Simulating Romeo Juliet Model Time units days • Scenario 6: Both Romeo and Juliet are indifferent. Initially, both feels 0 love units towards each other It is an unstable equilibrium

Run length = 12 days Simulating Romeo Juliet Model Time units days • Scenario 7: Juliet is indifferent. But initially, Romeo feels a very slight inclination, 1/100 th of love unit, for Juliet

Love-Hate Relationship ❤ ฀ ฀ It’s ❤ ฀ ฀ complicated! ♂ • Let’s call them Julien and Claire* • Claire is attracted to Julien when he shows no interest in her. When Julien begins to love her, he becomes pathetic in her eyes, and she develops a disgust for him. Julien is likewise attracted to Claire only when she gives him a cold shoulder and treats him with contempt. Then she becomes the prize that his ‘honor’ mandates that he ‘catch’. • What will happen when these two characters meet? *they are the protagonists from The Red and The Black by Stendhal

Julien Claire Model Julien Love for Claire Change in Juliens Love Initial Love of Julien for Claire Julien Reaction Claire Love for Julien Change in Claire Love Initial Love of Claire for Julien Claire Reaction • Julien’s Reaction = -1 • Claire Reaction = -1 • Both Julien’s reaction to Claire’s love and Claire’s reaction to Julien’s love are negative. Every unit of love that Julien displays to Claire decreases Claire’s love for Julien by one unit, and vice versa.

Run length = 12 months Simulating Julien Claire Model Time units months • Scenario 1: Julien initially likes Claire, but Claire dislikes him. Let Julien’s love be +1 love unit and Claire’s love be -1 love unit Trace the feedback loops

Run length = 12 months Simulating Julien Claire Model Time units months • Scenario 2: Suppose initially Julien loves Claire a little more than Claire loves Julien. ( Julien initially feels +1 love unit whereas Claire only feels 0.9 love units, that is, she likes him 10% less than he likes her ). What will happen? Zoom in to time period 0 and 2

Run length = 12 months Simulating Julien Claire Model Time units months • Scenario 3: Both Julien and Claire initially like each other. Initially, both feels +1 love units towards each other

Run length = 12 months Simulating Julien Claire Model Time units months • Scenario 4: Both Julien and Claire initially dis- like each other. Initially, both feels -1 love units towards each other

Run length = 12 months Simulating Julien Claire Model Time units months • Scenario 5: Both Julien and Claire are initially indifferent to each other. Initially, both feels 0 love units towards each other

Gone with the Wind* ฀ ฀ ❤ ฀ ❤ ❤ ❤ ฀ ฀ ฀ ฀ ♂ • Let’s call them Scarlet and Rhett* • When Rhett is indifferent to Scarlet, she is attracted to him. When Rhett is attracted to her, she scorns him. Rhett, however, becomes frustrated when Scarlet treats him with contempt. He is attracted to her when she is attracted to him, but he loses interest when she snubs him. • What will happen when these two meet? *Book by Margaret Mitchell

Gone with the wind model Rhetts Love for Scarlet Change in Rhetts Love Initial Love of Rhett for Scarlet Rhetts Reaction Scarlet Love Change in for Rhett Scarlets Love Initial Love of Scarlet for Rhett Scarlets Reaction • Rhett’s Reaction = + 1 • Scarlet's Reaction = -1 • Rhett’s reaction to Scarlet’s love is positive, while Scarlet’s reaction to Rhett’s love is negative.

Run length = 12 years Simulating GwtW Model Time units year • Scenario 1: Initially Scarlett and Rhett feel one unit of love for each other Trace the feedback loops

Run length = 12 years Simulating GwtW Model Time units year • Scenario 2: Initially Rhett loves Scarlet but Scarlet is indifferent to Rhett.

Run length = 12 years Simulating GwtW Model Time units year • Scenario 3: Initially Rhett likes Scarlet but Scarlet actively dislikes Rhett. What will happen to the two lovers?

Run length = 12 years Simulating GwtW Model Time units year • Scenario 4: Rhett and Scarlet are initially indifferent to each other. Will the system still oscillate?

Conclusions • We saw three scenarios • Romeo and Juliet (Classical Love Story) • Julien and Claire (Love-Hate relationship) • Scarlet and Rhett (Gone with the wind) • Generic structure Stock 1 • 2 nd order systems Change in Stock 1 Parameter 1 Stock 2 Change in Stock 2 Parameter 2

Conclusions • Generic structure for sustained oscillations • Oscillations are a feature of negative feedback loops in higher-order (two stocks or more) systems  Gone with wind model • No set of initial conditions can make the Romeo-Juliet or Julien-Claire models oscillate. • Romeo-Juliet and Julien-Claire models are driven by a positive feedback loop, which usually generates exponential behavior but can, in some exceptional cases, generate asymptotic behavior.

For you to try: Typical movie plot • Boy meet girl • He likes her on first sight, but she dislikes him • He woos her, but her dislike towards him grows • Then suddenly, • … she starts to reciprocate his love. • Model this.

References • Second-Order Systems, Prepared for the MIT System Dynamics in Education Project, by Leslie A. Martin (1998). Available online. • Vensim model made available via Moodle