Bdsm-ch4_behavior Of The System
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Business Dynamics and System Modeling
Chapter 4: Behavior of the System Pard Teekasap Southern New Hampshire University
Outline 1.Fundamental modes – Exponential growth – Goal seeking – Oscillation
2.Interaction of the fundamental modes – S-shaped growth – S-shaped growth with overshoot – Overshoot and collapse
What are the system behaviors come from? • The behavior arises from its structure • Structure consists of the feedback loops, stock and flow, and nonlinearities created by the interaction of the physical and institutional structure of the system
Common modes of behavior in dynamic systems Exponential Growth
Time
Oscillation
Time
Goal Seeking
S-shaped Growth
Time
Time
Growth with Overshoot
Overshoot and Collapse
Time
Time
Exponential Growth • Arises from positive feedback • Pure exponential growth has the constant doubling time • What is the examples of exponential growth?
Exponential Growth structure State of the System
Time
Net Increase Rate +
R
+ State of the System
Example of exponential growth US Real GDP
US Prison Population
8000
1200 AverageGrowthRate: 1926-1995:3.5%/year(doublingtime-20years) 1970-1995:6.8%/year(doublingtime-10years)
Thousand People
Billion 1992 $/Year
Average Growth Rate 3.45%/year DoublingTime-20years
4000
900
600
300
0 1850
1900
1950
0 1920
2000
1940
World Population
1980
2000
Transistors per Chip, Intel Microprocessors
6
6 Average Growth Rate: 1900 - 1950: 0.86%/year (doubling time - 80 years) 1950 - 1997: 1.76%/year (doubling time - 40 years)
Average Growth Rate: 33%/year (doubling time: - 2 years) 107
Million Transistors/Chip
Billion People
1960
6
4
4
2
2
3
104
Pentium
3
10
102
486
1965
1975
1985
1995
2000 Lower Bound
0 0
5
10
Upper Bound
0 1900
Pentium Pro
6
10
400
800
1200
1600
2000
4004
0 1965
1970
8080
1975
8086
80286
1980
386
1985
Best Fit Exponential
1990
1995
2000
Goal Seeking Goal State of the System
Time + State of the System B
Goal (Desired State of System)
Discrepancy
Corrective Action +
+
Characteristics of goal seeking • If the relationship between the size the gap and the corrective action is linear, the rate of adjustment is exactly proportional to the size of the gap and the resulting goalseeking behavior is exponential decay • Pure exponential decay is characterized by its half life • What are the examples of goal seeking behavior?
Example of goal-seeking behavior
Semiconductor Fabrication Defect Rate
Nuclear Plant Load Factor
1500
100 Start of TQM Program 80
1000 60 40
500
20 0 1987
25
1988
1989
1990
1991
0 1978
Television Share of All Advertising, US
1980
1982
1984
1986
1988
1990
1992
US Traffic Fatalities per Vehicle Mile 25
20
20
15
15
10
10
5
5
0 1950
1958
1967
1975
1983
1992
0 1920
1940
1960
1980
2000
Oscillation • The overshooting arises from the presence of significant time delays in the negative loop • However, most real world oscillations is not perfectly regular. You shouldn’t expect it to be • What are the examples of oscillation behavior?
Oscillation structure Goal State of the System Time Measurement, Reporting, and Perception Delays
Action Delays
+ State of the System Delay Delay
B
Goal (Desired State of System)
Discrepancy + Delay
Corrective Action +
Administrative and Decision Making Delays
Example of oscillation behavior US Real GDP Deviation From Trend 0.4
0.0
-0.4 1850
1900
Capacity Utilization, US Manufacturing
1950
2000
US Unemployment Rate
12
95
10 90
8 85
6 80
4 2
75 70 1945
1955
1965
1975
1985
1995
0 1945
1955
1965
1975
1985
1995
Process Point • When you see the behavior, you should know which type of loop is a dominant loop • E.g. if you observe exponential growth, you know there is at least one positive feedback (and possibly more) • However, there will be many negative loops as well. But the positive loops are dominant
S-shaped growth Carrying Capacity
State of the System
Time + Net Increase + Rate +
Fractional Net Increase Rate +
R
B
State of the System
Resource Adequacy +
Carrying Capacity
S-shaped growth condition • S-shaped growth happens only 1.The negative loops must not include any significant time delays 2.The carry capacity must be fixed
• Carry capacity is the capability of an environment to handle that variable • What are the examples of S-shaped behavior?
Example of S-shaped growth Growth of Sunflowers
300
200
100
0 0
100
14
28
US Cable Television Subscribers
42 Days
56
100
70
84
Adoption of Cardiac Pacemaker by Physicians
75
75 % of Households with TV Subscribing to Cable 50
50
25
25
0 1950
Cable Subscribers (Million Households) 1960
1970
1980
1990
2000
0 1960
1962
1964
1966
1968
1970
1972
S-shaped growth with overshoot • S-shaped structure with significant time delays in the negative loops • Time delays in the negative loops lead to the possibility that the state of the system will overshoot and oscillate around the carrying capacity • What are the examples of S-shaped growth with overshoot?
S-shaped growth with overshoot structure Carrying Capacity
State of the System Time Net Increase Rate + + Fractional Net Increase Rate +
+ State of the R System Delay B
Delay
Resource Adequacy +
Carrying Capacity
Example of S-shaped growth with overshoot Population of London 10 8 6 4 2 0 1800
1850
1900
1950
2000
US Aluminum Production
5000
2500
0 1900
1920
1940
1960
1980
2000
Overshoot and Collapse • Carrying capacity is reduced by the variables • E.g. the ability of the environment to support a growing population is eroded or consumed by the population itself • If there is no regeneration of the carrying capacity, the equilibrium of the system is extinction • What are the examples of overshoot and collapse?
Overshoot and collapse structure Carrying Capacity
State of the System Time
Net Increase + Rate +
R
+
+ State of the System
Consumption/ Erosion of Carrying Capacity
B Fractional Net Increase Rate +
B
Resource Adequacy +
Carrying Capacity
Example of overshoot and collapse New England Haddock Catch
150
40
Net Change in World Nuclear Power Capacity
30 100 20 50 10
0 1880
2.0
1900
1920
1940
1960
1980
2000
Sales of the Atari Corporation
0 1950
30
1.0
20
0.5
10
1978
1980
1982
1984
1986
0 1975
1970
1980
1990
2000
1983
1985
Silver Prices
40
1.5
0.0 1976
1960
1977
1979
1981
What are the structures for these exponential growth behaviors? US Real GDP
US Prison Population
8000
1200 AverageGrowthRate: 1926-1995:3.5%/year(doublingtime-20years) 1970-1995:6.8%/year(doublingtime-10years)
Thousand People
Billion 1992 $/Year
Average Growth Rate 3.45%/year DoublingTime-20years
4000
900
600
300
0 1850
1900
1950
0 1920
2000
1940
World Population
1980
2000
Transistors per Chip, Intel Microprocessors
6
6 Average Growth Rate: 1900 - 1950: 0.86%/year (doubling time - 80 years) 1950 - 1997: 1.76%/year (doubling time - 40 years)
Average Growth Rate: 33%/year (doubling time: - 2 years) 107
Million Transistors/Chip
Billion People
1960
6
4
4
2
2
5
10
3
104
Pentium
3
10
102
486
1965
1975
1985
1995
2000 Lower Bound
0 0
10
Upper Bound
0 1900
Pentium Pro
6
400
800
1200
1600
2000
4004
0 1965
1970
8080
1975
8086
80286
1980
386
1985
Best Fit Exponential
1990
1995
2000
Basic positive feedbacks responsible for economic growth
Expanding the model to include investment and births
Simple model of the demographic transition
First-cut model to explain growth in prison population
Prison population model expanded to include hypothesized social feedback
Prison population model expanded to include rewards and risk of crime
Selected positive feedbacks underlying Moore’s Law
What are the structures underlying these goal-seeking behaviors? Semiconductor Fabrication Defect Rate
1500
Nuclear Plant Load Factor
100
Start of TQM Program 80 1000 60 40
500
20 0 1987
25
1988
1989
1990
1991
0 1978
Television Share of All Advertising, US
1980
1982
1984
1986
1988
1990
1992
US Traffic Fatalities per Vehicle Mile 25
20
20
15
15
10
10
5
5
0 1950
1958
1967
1975
1983
1992
0 1920
1940
1960
1980
2000
Process improvement efforts – PDCA
Process improvement for nuclear plant load
Feedbacks acting to improve automobile safety
Demand and supply for TV ads
TV ads model expands to include the audience annoyance loop
TV ads model expands to include couch potato and program quality
What are the structures underlying these oscillation behaviors? US Real GDP Deviation From Trend
0.4
0.0
-0.4 1850
1900
Capacity Utilization, US Manufacturing
1950
2000
US Unemployment Rate
12
95
10 90
8 85
6 80
4 2
75 70 1945
1955
1965
1975
1985
1995
0 1945
1955
1965
1975
1985
1995
Negative feedbacks and delays contributing to the business cycle
Next Week • Chapter 6 • Research Proposal • 1 paragraph summarize of Navid’s paper
Chapter 4: Behavior of the System Pard Teekasap Southern New Hampshire University
Outline 1.Fundamental modes – Exponential growth – Goal seeking – Oscillation
2.Interaction of the fundamental modes – S-shaped growth – S-shaped growth with overshoot – Overshoot and collapse
What are the system behaviors come from? • The behavior arises from its structure • Structure consists of the feedback loops, stock and flow, and nonlinearities created by the interaction of the physical and institutional structure of the system
Common modes of behavior in dynamic systems Exponential Growth
Time
Oscillation
Time
Goal Seeking
S-shaped Growth
Time
Time
Growth with Overshoot
Overshoot and Collapse
Time
Time
Exponential Growth • Arises from positive feedback • Pure exponential growth has the constant doubling time • What is the examples of exponential growth?
Exponential Growth structure State of the System
Time
Net Increase Rate +
R
+ State of the System
Example of exponential growth US Real GDP
US Prison Population
8000
1200 AverageGrowthRate: 1926-1995:3.5%/year(doublingtime-20years) 1970-1995:6.8%/year(doublingtime-10years)
Thousand People
Billion 1992 $/Year
Average Growth Rate 3.45%/year DoublingTime-20years
4000
900
600
300
0 1850
1900
1950
0 1920
2000
1940
World Population
1980
2000
Transistors per Chip, Intel Microprocessors
6
6 Average Growth Rate: 1900 - 1950: 0.86%/year (doubling time - 80 years) 1950 - 1997: 1.76%/year (doubling time - 40 years)
Average Growth Rate: 33%/year (doubling time: - 2 years) 107
Million Transistors/Chip
Billion People
1960
6
4
4
2
2
3
104
Pentium
3
10
102
486
1965
1975
1985
1995
2000 Lower Bound
0 0
5
10
Upper Bound
0 1900
Pentium Pro
6
10
400
800
1200
1600
2000
4004
0 1965
1970
8080
1975
8086
80286
1980
386
1985
Best Fit Exponential
1990
1995
2000
Goal Seeking Goal State of the System
Time + State of the System B
Goal (Desired State of System)
Discrepancy
Corrective Action +
+
Characteristics of goal seeking • If the relationship between the size the gap and the corrective action is linear, the rate of adjustment is exactly proportional to the size of the gap and the resulting goalseeking behavior is exponential decay • Pure exponential decay is characterized by its half life • What are the examples of goal seeking behavior?
Example of goal-seeking behavior
Semiconductor Fabrication Defect Rate
Nuclear Plant Load Factor
1500
100 Start of TQM Program 80
1000 60 40
500
20 0 1987
25
1988
1989
1990
1991
0 1978
Television Share of All Advertising, US
1980
1982
1984
1986
1988
1990
1992
US Traffic Fatalities per Vehicle Mile 25
20
20
15
15
10
10
5
5
0 1950
1958
1967
1975
1983
1992
0 1920
1940
1960
1980
2000
Oscillation • The overshooting arises from the presence of significant time delays in the negative loop • However, most real world oscillations is not perfectly regular. You shouldn’t expect it to be • What are the examples of oscillation behavior?
Oscillation structure Goal State of the System Time Measurement, Reporting, and Perception Delays
Action Delays
+ State of the System Delay Delay
B
Goal (Desired State of System)
Discrepancy + Delay
Corrective Action +
Administrative and Decision Making Delays
Example of oscillation behavior US Real GDP Deviation From Trend 0.4
0.0
-0.4 1850
1900
Capacity Utilization, US Manufacturing
1950
2000
US Unemployment Rate
12
95
10 90
8 85
6 80
4 2
75 70 1945
1955
1965
1975
1985
1995
0 1945
1955
1965
1975
1985
1995
Process Point • When you see the behavior, you should know which type of loop is a dominant loop • E.g. if you observe exponential growth, you know there is at least one positive feedback (and possibly more) • However, there will be many negative loops as well. But the positive loops are dominant
S-shaped growth Carrying Capacity
State of the System
Time + Net Increase + Rate +
Fractional Net Increase Rate +
R
B
State of the System
Resource Adequacy +
Carrying Capacity
S-shaped growth condition • S-shaped growth happens only 1.The negative loops must not include any significant time delays 2.The carry capacity must be fixed
• Carry capacity is the capability of an environment to handle that variable • What are the examples of S-shaped behavior?
Example of S-shaped growth Growth of Sunflowers
300
200
100
0 0
100
14
28
US Cable Television Subscribers
42 Days
56
100
70
84
Adoption of Cardiac Pacemaker by Physicians
75
75 % of Households with TV Subscribing to Cable 50
50
25
25
0 1950
Cable Subscribers (Million Households) 1960
1970
1980
1990
2000
0 1960
1962
1964
1966
1968
1970
1972
S-shaped growth with overshoot • S-shaped structure with significant time delays in the negative loops • Time delays in the negative loops lead to the possibility that the state of the system will overshoot and oscillate around the carrying capacity • What are the examples of S-shaped growth with overshoot?
S-shaped growth with overshoot structure Carrying Capacity
State of the System Time Net Increase Rate + + Fractional Net Increase Rate +
+ State of the R System Delay B
Delay
Resource Adequacy +
Carrying Capacity
Example of S-shaped growth with overshoot Population of London 10 8 6 4 2 0 1800
1850
1900
1950
2000
US Aluminum Production
5000
2500
0 1900
1920
1940
1960
1980
2000
Overshoot and Collapse • Carrying capacity is reduced by the variables • E.g. the ability of the environment to support a growing population is eroded or consumed by the population itself • If there is no regeneration of the carrying capacity, the equilibrium of the system is extinction • What are the examples of overshoot and collapse?
Overshoot and collapse structure Carrying Capacity
State of the System Time
Net Increase + Rate +
R
+
+ State of the System
Consumption/ Erosion of Carrying Capacity
B Fractional Net Increase Rate +
B
Resource Adequacy +
Carrying Capacity
Example of overshoot and collapse New England Haddock Catch
150
40
Net Change in World Nuclear Power Capacity
30 100 20 50 10
0 1880
2.0
1900
1920
1940
1960
1980
2000
Sales of the Atari Corporation
0 1950
30
1.0
20
0.5
10
1978
1980
1982
1984
1986
0 1975
1970
1980
1990
2000
1983
1985
Silver Prices
40
1.5
0.0 1976
1960
1977
1979
1981
What are the structures for these exponential growth behaviors? US Real GDP
US Prison Population
8000
1200 AverageGrowthRate: 1926-1995:3.5%/year(doublingtime-20years) 1970-1995:6.8%/year(doublingtime-10years)
Thousand People
Billion 1992 $/Year
Average Growth Rate 3.45%/year DoublingTime-20years
4000
900
600
300
0 1850
1900
1950
0 1920
2000
1940
World Population
1980
2000
Transistors per Chip, Intel Microprocessors
6
6 Average Growth Rate: 1900 - 1950: 0.86%/year (doubling time - 80 years) 1950 - 1997: 1.76%/year (doubling time - 40 years)
Average Growth Rate: 33%/year (doubling time: - 2 years) 107
Million Transistors/Chip
Billion People
1960
6
4
4
2
2
5
10
3
104
Pentium
3
10
102
486
1965
1975
1985
1995
2000 Lower Bound
0 0
10
Upper Bound
0 1900
Pentium Pro
6
400
800
1200
1600
2000
4004
0 1965
1970
8080
1975
8086
80286
1980
386
1985
Best Fit Exponential
1990
1995
2000
Basic positive feedbacks responsible for economic growth
Expanding the model to include investment and births
Simple model of the demographic transition
First-cut model to explain growth in prison population
Prison population model expanded to include hypothesized social feedback
Prison population model expanded to include rewards and risk of crime
Selected positive feedbacks underlying Moore’s Law
What are the structures underlying these goal-seeking behaviors? Semiconductor Fabrication Defect Rate
1500
Nuclear Plant Load Factor
100
Start of TQM Program 80 1000 60 40
500
20 0 1987
25
1988
1989
1990
1991
0 1978
Television Share of All Advertising, US
1980
1982
1984
1986
1988
1990
1992
US Traffic Fatalities per Vehicle Mile 25
20
20
15
15
10
10
5
5
0 1950
1958
1967
1975
1983
1992
0 1920
1940
1960
1980
2000
Process improvement efforts – PDCA
Process improvement for nuclear plant load
Feedbacks acting to improve automobile safety
Demand and supply for TV ads
TV ads model expands to include the audience annoyance loop
TV ads model expands to include couch potato and program quality
What are the structures underlying these oscillation behaviors? US Real GDP Deviation From Trend
0.4
0.0
-0.4 1850
1900
Capacity Utilization, US Manufacturing
1950
2000
US Unemployment Rate
12
95
10 90
8 85
6 80
4 2
75 70 1945
1955
1965
1975
1985
1995
0 1945
1955
1965
1975
1985
1995
Negative feedbacks and delays contributing to the business cycle
Next Week • Chapter 6 • Research Proposal • 1 paragraph summarize of Navid’s paper
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