1. SYSTEM DYNAMICS
Dr. John Bradford

2. Feedback
• Feedback Loop: occurs when changes
generate effects that then influence the
original causes of the change, making
subsequent change either more (+) or less (-) likely.
Effect Cause

3. Feedback
Two types of Feedback: Positive Feedback
1. Positive (reinforcing, amplifying):
Initial changes become amplified or
magnified over time; patterns are Population Births
reinforced. + +
– Examples: exponential population
growth; nuclear explosion; ‘rich getting
richer’, etc.
2. Negative (counteracting, Negative Feedback
balancing):
Initial changes are counteracted or
Force of
balanced out, so that conditions remain Jump up
Gravity
relatively stable. +
-
– Examples: homeostasis; a thermostat;
“what goes up, must come down”, etc.

4. Stocks and Flows
Stock
f lowing
Stocks
 “Nouns” that indicate conditions or states of
being at a point in time.
 Stocks are things that accumulate over time from flows
Flows
 “Verbs” that represent activities or processes,
which exist over time.
 Flows fill and drain stocks, that is, they update the
magnitude of stocks.

5. Stock-Flow diagram of Feedback
 Stock-flow structure of “Positive” (Reinforcing) and
“negative” (counteracting) feedback systems:
Reinforcing Loop: Counteracting Loop:
Exponential growth Exponential decay
Populat ion
Populat ion
declining
growing
growt h
decline
rat e ~ rat e
A feedback loop occurs whenever a change in the magnitude of a stock
in turn affects a flow into or out of that same stock.

6. Feedback loop Dynamics
 When both positive and negative feedback are present in
the same system, four possibilities arise:
1. exponential growth: the reinforcing loop will dominate the
counteracting loop.
2. exponential decay: the counteracting loop will dominate the
dominate the reinforcing loop.
3. equilibrium: they balance each other out.
4. Oscillation: it goes up, then down, up and down, …
Population
growing declining
growth
rate decline
~ rate

7. Dynamics of Depletion: Overshoot and Collapse
The Stock-Flow Structure looks The Behavioral Dynamic looks
like this: like this:
Populat ion
growing declining
Population: 1 - 2 - 3 -
1: 1800
growt h
rat e decline 3
~ rat e
Resource
consuming 2
1: 900
3
2
1
1
2 3
1 3
1: 0 1 2
~ 0.00 5.00 10.00 15.00 20.00
Page 1 Years 1:16 AM Wed, Feb 24, 2010
resources
per pop Sensitiv ity Results f or Population

8. Dynamics of Depletion: Overshoot and Rebound
 If the resource is renewable, it is possible that it can rebound, but
the in order for this to occur, the resources per population must go
to zero before Resource does,
 In the context of economics, this periodic growth, collapse, and
regrowth can be considered as a process of Schumpeterean
“creative destruction”
Population
growing declining
1: Population
1: 4000
growth
rate
decline
Resources ~ 1: 2000
consuming rate
regenerating
1 1
1
1: 0 1
~ 0.00 15.00 30.00 45.00 60.00
Page 1 Years 10:10 AM Wed, Mar 03, 2010
regeneration
Population
rate
~
resources
per pop

9. Stock-flow diagram of system exhibiting overshoot
behavior
Po pul atio n
i ni ti al 10
be in g born
dyin g
De ath rate
D=1-R(t)/R(0)
Bi rth Ra te
co nsumi ng
Re sou rce
co nsumpti on
per cap ita

10. Overshoot and Collapse of Population
Population: 1 - 2 - 3 - 4 - 5 -
1: 1800
3
2
1: 900
3 4
2
1 5
5
4 1
2 3
1 3
1: 0
4 5 1 2 4 5
0.00 5.00 10.00 15.00 20.00
Page 1 Years 2:06 PM Tue, Mar 02, 2010
Sensitiv ity Results f or Population