Simple positive feedback

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Simple positive feedback

• Example
• Bank balance
• Interest Payments Bank Balance Interest Rate
• Positive feedback the stock will continue to
  increase (exponential growth, y aXebx )
• Initial balance 10, interest rate 10 per year

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Simple positive feedback

• Draw the flow diagram?

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Simple positive feedback

• Positive feedback can not continue forever (there
  are always limits food / space /)
• Limits to Growth
• Other positive feedback examples
• Cell division
• Spread of rumor
• Growth of a company
• Spread of forest fire

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Simple positive feedback
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Simple negative feedback

• Negative feedback exhibits goal - seeking
  behavior.
• Example Coffee Cooling (non zero goal)

• Causal loop diagram (signs) Flow
  diagram

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Simple negative feedback

• Solve using initial temp 50oC
• decline in temp ?
• Common sense assumption - cooling stops at room
  temperature.
• decline in temp (temperature - room
  temperature) / T
• Where T is the cooling constant (function of
  coffee container surface area etc.).
• For room temperature 20oC and T 5 min
• Decline in temp (50-20)/5 6oC/min

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Simple negative feedback

• The above diagram has one problem much of the
  detail involved in the rate (decline in
  temperature) equation is hidden in single arrow.
• A better representation of this is to define a
  new variable named difference.
• This is called an auxiliary variable (very useful
  in formulating complex rate equations).

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Simple negative feedback
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Simple negative feedback

• A conserved quantity has the property that it is
  never created or destroyed (within its system)
  it is only moved around.

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S-shaped growth

• Known as logistic or sigmoid growth.
• It is a common type of behavior which combines
  both exponential (positive) and asymptotic
  (negative) growth.
• Population trends of various plant and animals
  typify S-shaped patterns.

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S-shaped growth
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S-shaped growth

• The goal persists indefinitely and is called
  stable equilibrium.
• Prior to the growth (at level value of zero) the
  system rests at unstable equilibrium.
• The slightest disturbance produces a rate value
  other than zero (the system level increases).

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S-shaped growth

• Draw a flow diagram for the problem in Assignment
  1.

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Transferability of structures

• Up to now you might have noticed some
  similarities amongst models.
• For example the Bathtub and Population models.
• This phenomenon occurs all the time in system
  dynamics and it is known as Transferability of
  Structures.
• Structures common to several systems are called
  generic structures.

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First order positive feedback

• Generic structure

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First order positive feedback

• Generic equations
• stock(t) stock(t-dt) flow dt units
• flow stock compounding_factor
  units/time
• compounding_factor a constant
  units/unit/time
• OR
• flow stock / time_constant units/time
• time_constant a constant time

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First order positive feedback

• Generic model behavior

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First order positive feedback
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First order negative feedback

• Generic structure

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First order negative feedback

• Generic equations
• stock(t) stock(t-dt) (-flow) dt units
• flow adjustment_time draining_fraction
  units/time
• adjustment_gap stock - goal_for_stock
  units
• draining_fraction a constant 1/time
• goal_for_stock a constant units
• OR
• flow adjustment_gap / time_constant
  units/time
• time_constant a constant time

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First order negative feedback

• Generic behavior

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First order negative feedback