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

Nov 25, 2023 288 likes •582 views

Dynamics of Love IE604: System Dynamics Modeling and Analysis Jayendran Venkateswaran, IIT Bombay 14 th February Special Classical Love Story Lets call them Romeo and Juliet Romeo and Juliet are madly in love

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Dynamics of Love

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

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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?

฀ ฀

❤฀ ❤฀

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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.

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Romeo Juliet Model

  • 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”

Romeos Love for Juliet Change in Romeos Love Juliets Love for Romeo Change in Juliets Love Romeos Reaction Juliets Reaction Initial Love of Romeo for Juliet Initial Love of Juliet for Romeo

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Simulating Romeo Juliet Model

  • 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 Run length = 12 days Time units days Trace the feedback loops

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Simulating Romeo Juliet Model

  • 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 Time units days

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Simulating Romeo Juliet Model

  • 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 Time units days

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Simulating Romeo Juliet Model

  • 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 Time units days

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Simulating Romeo Juliet Model

  • 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 Time units days

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Simulating Romeo Juliet Model

  • Scenario 6: Both Romeo and Juliet are indifferent. Initially, both

feels 0 love units towards each other

Run length = 12 days Time units days It is an unstable equilibrium

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Simulating Romeo Juliet Model

  • Scenario 7: Juliet is indifferent. But initially, Romeo feels a very

slight inclination, 1/100th of love unit, for Juliet

Run length = 12 days Time units days

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Love-Hate Relationship

  • 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?

฀ ฀

❤ ❤

฀ ♂ ฀

It’s complicated!

*they are the protagonists from The Red and The Black by Stendhal

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Julien Claire Model

Julien Love for Claire Change in Juliens Love Claire Love for Julien Change in Claire Love Julien Reaction Claire Reaction Initial Love of Julien for Claire Initial Love of Claire for Julien

  • 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.

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Simulating Julien Claire Model

  • 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

Run length = 12 months Time units months Trace the feedback loops

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Simulating Julien Claire Model

  • 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? Run length = 12 months Time units months

Zoom in to time period 0 and 2

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Simulating Julien Claire Model

  • Scenario 3: Both Julien and Claire initially like each other.

Initially, both feels +1 love units towards each other

Run length = 12 months Time units months

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Simulating Julien Claire Model

  • Scenario 4: Both Julien and Claire initially dis-like each other.

Initially, both feels -1 love units towards each other

Run length = 12 months Time units months

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Simulating Julien Claire Model

  • Scenario 5: Both Julien and Claire are initially indifferent to

each other. Initially, both feels 0 love units towards each other

Run length = 12 months Time units months

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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

฀

❤

฀

❤

฀

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Gone with the wind model

  • 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.

Rhetts Love for Scarlet Change in Rhetts Love Scarlet Love for Rhett Change in Scarlets Love Rhetts Reaction Scarlets Reaction Initial Love of Rhett for Scarlet Initial Love of Scarlet for Rhett

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Simulating GwtW Model

  • Scenario 1: Initially Scarlett and Rhett feel one unit of love for

each other

Run length = 12 years Time units year Trace the feedback loops

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Simulating GwtW Model

  • Scenario 2: Initially Rhett loves Scarlet but Scarlet is indifferent

to Rhett.

Run length = 12 years Time units year

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Simulating GwtW Model

  • Scenario 3: Initially Rhett likes Scarlet but Scarlet actively

dislikes Rhett. What will happen to the two lovers?

Run length = 12 years Time units year

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Simulating GwtW Model

  • Scenario 4: Rhett and Scarlet are initially indifferent to each
  • ther. Will the system still oscillate?

Run length = 12 years Time units year

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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
  • 2nd order systems

Stock 1 Change in Stock 1 Stock 2 Change in Stock 2 Parameter 1 Parameter 2

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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

  • scillate.
  • 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.

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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.
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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