Reasoning About Complex Systems

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Reasoning About Complex Systems
Feedback Loops, Equations, and BOTG
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In this lecture...

• Open/Closed Systems
• Open-Loop and Closed-Loop
• Positive/Negative Feedback Loops
• Equations
• BOTG Behavior Over Time Graphs

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Reading Materials

• An Introduction to Feedback, by Leslie A.
  Martin
• First-Order Positive Feedback, by Albin and
  Choudhari
• First-Order Negative Feedback, by Albin

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Open/Closed Systems

• Open - Interacts with its environment
• Closed - Does not interact with its environment

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Closed System
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Open System
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Open-Loop Closed-Loop

• Open-Loop Components are linked in a simple
  chain
• Closed-Loop Contains feedback loops where a
  change in a stock induces a further change in the
  same stock

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Open Loop System
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Closed Loop System
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Types of Feedback Loops

• A reinforcing loop tends to accentuate a change
  in a stock
• causes an initial increase to go up even more
• causes a drop to drop even further
• A balancing loop tends to counteract a change in
  a stock
• acts to reverse an initial increase
• acts to rebound from an initial decrease

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Reinforcing Feedback Loops

• An increase in a stock tends to act to cause a
  further increase in the same stock
• A decrease in a stock tends to act to cause a
  further decrease in the same stock
• There may be a number of stock and flow links
  in the feedback chain
• The effect may occur after a delay which may be
  considerable in length
• Also called a positive loop

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Generic Reinforcing Loop
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Reinforcing Feedback Loop
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Balancing Feedback Loops

• An increase in a stock tends to act to cause a
  decrease in the same stock
• An decrease in a stock tends to act to cause a
  increase in the same stock
• There may be a number of stock and flow links
  in the feedback chain
• The effect may occur after some delay which may
  be considerable in length
• Also called a negative feedback loop

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Balancing Feedback Loop(Inflow)
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From Lab 1 Balancing Feedback Loop
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Equations

• The initial value for Temperature is 60.
• Assign 100 to "Desired Temperature"
• Set "Gap" equal to "Desired Temperature" minus
  "Temperature".
• Set "Change in Temperature" equal to "Gap"
  divided by 10.

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BOTG Behavior over Time Graph
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Generic Balancing Loop(outflow)
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From Lab 2
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• Write the equations for the population model

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Sample BOTG
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Identifying Loops

• Start at a Stock
• Follow an information arrow away from the stock
• Follow the effect of flows
• Upstream for outflows
• Downstream for inflows
• Keep following information arrows and the effect
  of flows
• If you get back to the original stock you have
  identified a feedback loop
• Do this for all stocks and all information arrows
  leaving them

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Identifying Loops System 1
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Analyzing Loops 1

• Start with a Stock in the loop
• Hypothesize that the stock goes up
• Walk through the loop following information
  arrows and the effects of flows.
• At each step determine the systems effect
• if the stock went up then this variable/flow
  will go up/down
• if this variable goes up/down then this
  variable/flow will go up/down
• if this flow goes up/down then this stock will
  go up/down

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Analyzing Loops 2

• When you have traced through the feedback loop
  all the way back to the original stock
• the loop is reinforcing if the resulting
  influence on the original stock is to cause it to
  increase
• the loop is balancing if the resulting influence
  on the original stock is to cause it to decrease

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System 1
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Review of Feedback Loops

• A reinforcing loop tends to accentuate a change
  in a stock
• causes an initial increase to go up even more
• causes an initial drop to drop even further
• A balancing loop tends to counteract a change in
  a stock
• acts to reverse an initial increase
• acts to rebound from an initial decrease

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System 2 - Determine the types of the feedback
loops in the following sample system
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System 2
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System 3 - Determine the types of the feedback
loops in the following sample system
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System 3
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Try

• Answering the questions in the lab activities.
• Modeling the following scenario
• You open a bank account with an initial deposit
  of 1000. Each week you deposit your paycheck
  (150) and pay your bills (125). You earn
  interest on the account at the rate of 0.2 per
  week. You spend 4 of the account balance per
  week on personal items.
• Identify feedback loops
• Simulate and look at the BOTG
• Will you run out of money? If so when?

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End