What is simulation ?

What is simulation ?

"... conceive simulation as a special case of a more general and conceptually richer paradigm of model-based activities ..“ (Ören

1984)

"Simulation is the process of designing a model of a real system and conducting experiments with this model for the purpose either of understanding the behavior of the system or of evaluating various

strategies ... for the operation of the system“

(Shannon 1975)

Work definitionsMODEL:

A model is a goal oriented representation of a system that exists in reality or can be realized

Symbolic Language

Real World

Model

(Theory )

objects

Interpretations

Work definitions

Computermodel:A computer model = an algorithm = of a system

that can be realized in the real world

Simulation:Simulation is stepping through a computer

model with the purpose to describe the behavior of a real system

Paradigms Programs of Research

"A scientific view on the world guided by a methodology .... disciplinary matrix ... symbolic generalization .. shared

commitment in a particular model"(Kuhn 1970, 1977)

 "The history of science has been and should be a history of

completing research programs (or if you wish paradigm's ), but it has not been and must become a succession of periods of normal

science: the sooner competition starts, the better for progress. Theoretical pluralism is better then theoretical monism"

(Lakatos 1970) 

A successful research program is one that generates a series of theories (a problem shift) which consistently is theoretically

progressive and intermittently is empirically progressive. Mature science consists of research programs, whereas immature science

consist of a "mere patched up pattern of trial and error"(Lakatos 1970)

Paradigms of Simulation

• Discrete opposite Continue

• Stochastic opposite Deterministic

* Recursive causality

opposite

NON recursive causality

* Linear opposite Non linear

View on Causality

Non RecursiveOneway Traffic Cause Effect

Reichenbach, Popper, traditional view in Methodological TextbooksAnd view of most SEM modelers

+ Linear dependency

Effect = constant*CausePearson-correlationLineair regression

Path models

AB

C

E F+ +

+

+

++

View on Causality

RecursiveCircle between Cause and Effect

Cause Effect

t

View on Causality System Dynamics

• Feedback loop

Cause Effect

Goal

t

View on Causality System Dynamics

Feedback (Wiener, Forrester) 

Goal searching systemInteraction between variables

Behavior

Norms

DBehavior

View on Causality System Dynamics

A(t) B(t+t)A(t+2t)

t

Mathematical viewed it leads to a:Recursive Difference equation

D A/ D t = F(A, t)

Modeling Recursive CausalitySYSTEMDYNAMICS

Holistic approach, feedback(Forester, Meadows)

&From Verbal Description

toMathematical models of Causality

(Blalock)

+SOFTWARE STELLA

(Meadows, Richmond)

UserfriendlyModeling of Causality

By means of Graphic Symbols

Approach Stella FROM VERBAL DESCRIPTION

VIACAUSAL DIAGRAMs

ANDFEEDBACK DESCRIPTIONS

  VIA 

 FLOW DIAGRAMS

TO  

DIFFERENTIAL EQUATIONS that are

 OPERATIONAL COMPUTERMODELS

STELLA

A Demonstration

From Verbal Description to

Causal Diagrams

An Example

Verbal Description:

Money put on the bank produces after some time interest, that result in more

capital on the bank, producing after another period of time -supposing a

fixed rate of interest- more interest, and as a consequence more capital, and so

on.

From Verbal Description to

Causal Diagrams

Causal Diagram

+

+

++

Capital

Interest

Rate of interest

Another example

Causal diagram

-

+

+ +

Verbal Description? An Exercise

Number of population

Number of deaths Newborns

BirthrateDeath rate

Verbal Description:

The number of the newborns and the number of deaths are proportional to the number of the population. The

number of newborns is proportional to the birthrate. The number of deaths is

proportional to the deathrate. Newborns add up the population. The number of death subtracts from the population

(alternative statements are possible)

CAUSAL DESCRIPTIONSCausal diagram

A

B C

-

+

+ +

D E

++

CAUSALE DESCRIPTIONS Causal Matrix

Cause A B C D E

A   - +    

B +     +  

C +       +

D          

E          

Effect

STELLA

• AN EXERCISE

– GROWTH OF CAPITAL

FROM CAUSAL DIAGRAMS AND FEEDBACK DESCRIPTIONS

VIA A FLOWDIAGRAM

Capital

Interest

RateofInterest

To a DIFFERENCE EQUATION

Capital*restRateofInteyearTime

Capital

FROM CAUSAL DIAGRAMS AND FEEDBACK DESCRIPTIONS

VIA a FLOW DIAGRAM

FROM CAUSAL DIAGRAMS AND FEEDBACK DESCRIPTIONS

VIA a FLOW DIAGRAM

and a DIFFERENCE EQUATION

To a DIFFERENTIAL EQUATION (t 0)

IN STELLA NOTATIONCapital(t) = Capital(t - dt) + (Interest) * dt

INIT Capital = 1000INFLOWS:

Interest = Capital*RateofInterestRateofInterest = 0.05

Capital*restRateofIntedTime

dCapital

Differential Equations

Linear Differential Equations– An Exercise

– Growth of a Population

Differential Equations

Non Linear Differential Equations– An Exercise

– Limited Growth of a Population

Differential Equations

Non Linear Differential Equations– An Exercise

Spread of a disease

WhyNon Linear Differential Equations

in Social Sciences ?

Behavior

Norms

DBehavior

Behavior of an Individual

Feedback Most of time non linear

WhyNon Linear Differential Equations

in Social Sciences ?

Behavior person A

Norms

Interaction between Individuals

Feedback Most of time non linear

Behavior person B

Differential Equations

Non Linear Differential Equations– An Exercise

Coupled Limited Growth

An example of InteractionGP Patient Communication

A simplified kernel of our ModelHow well do we understand the complaint?

What is the information content of this understanding ?

GPvaluationComplaint

driveGP

RatedriveGP

PatientvaluationComplaint

drivePatient

ratedrivePatient

mpltpPatientToGP

mltplierGPtoPatient

GPvaluationComplaint

driveGP

RatedriveGP

PatientvaluationComplaint

drivePatient

ratedrivePatient

mpltpPatientToGP

mltplierGPtoPatient

19: 48 Tue 25 Sep 2007

0. 00 10. 00 20. 00 30. 00 40. 00

Tim e

1:

1:

1:

0, 00

30, 00

60, 00

1: G Pvaluat ionCom plaint

1 1

1

1

G r aph 1 ( Unt it led)

Limited growth: when the GP has said and ask enough about what is in a biomedical sense going on, he or she will stop

talking and stay on a stable valuation of the complaint

When patients need to understand

19: 48 Tue 25 Sep 2007

0. 00 10. 00 20. 00 30. 00 40. 00

Tim e

1:

1:

1:

0, 00

30, 00

60, 00

1: G Pvaluat ionCom plaint

1 1

1

1

G r aph 1 ( Unt it led)

Limited growth: when the Patient has asked and said enough about what is in a biomedical sense going on,

he or she will stop talking and stay on a stable valuation of the complaint

But those two interact!

20:06 Tue 25 Sep 2007

0.00 10.00 20.00 30.00 40.00

Time

1:

1:

1:

0,00

20,00

40,00

1: GPvaluationComplaint

1

1

1

1

Graph 1 (Untitled)

What happens when a GP has a very strong drive to present his/her message and the patient has a very strong drive to tell

their story?GP drive=Patient drive=2

Unlimited number of outcomes: CHAOS

CHAOSThe logic of It ?

Looking to one side of the coupling

To A plot of outcomes with varying parameter r(of the GPdrive in our case; in this case a normalized graph and r as

transformed parameter)

Coupled Growers

population1

growth1

population 2

growth parameter1

growth 2

growth parameter 2

couplingf actor

Coupled Growersgrowth Parameter 1= 3; growth Parameter 2 = 1

Coupling factor = 0.1

Population1

Population2

5:05 PM Wed, Aug 13, 2008

0.00 10.00 20.00 30.00 40.00

Time

1:

1:

1:

0.00

1.00

2.00

1: population1

1

1

1

1

population1: p1 (Unti tled)

3:12 PM Tue, Aug 19, 2008

0.00 10.00 20.00 30.00 40.00

Time

1:

1:

1:

0.00

1.00

2.00

1: population 2

1

1

1

1

population2 (Unti tled)

Coupled Growersgrowth Parameter 1= 3; growth Parameter 2 = 1

Coupling factor = 0.3

Population1

Population2

5:05 PM Wed, Aug 13, 2008

0.00 10.00 20.00 30.00 40.00

Time

1:

1:

1:

0.00

1.00

2.00

1: population1

1

1

1

1

population1: p1 (Unti tled)

3:13 PM Tue, Aug 19, 2008

0.00 10.00 20.00 30.00 40.00

Time

1:

1:

1:

0.00

1.00

2.00

1: population 2

1

1

1

1

population2 (Unti tled)

Coupled Growersgrowth Parameter 1= 3; growth Parameter 2 = 1

Coupling factor = 0.5

Population1

Population2

2:53 PM Tue, Aug 19, 2008

0.00 10.00 20.00 30.00 40.00

Time

1:

1:

1:

0.00

1.00

2.00

1: population 2

1

1 1

1

population2 (Unti tled)

5:05 PM Wed, Aug 13, 2008

0.00 10.00 20.00 30.00 40.00

Time

1:

1:

1:

0.00

1.00

2.00

1: population1

1

1

1

1

population1: p1 (Unti tled)

Coupled Growersgrowth Parameter 1= 3; growth Parameter 2 = 1

Coupling factor = 1

Population1

Population2

2:54 PM Tue, Aug 19, 2008

0.00 10.00 20.00 30.00 40.00

Time

1:

1:

1:

0.00

1.00

2.00

1: population 2

1

11

1

population2 (Unti tled)

5:05 PM Wed, Aug 13, 2008

0.00 10.00 20.00 30.00 40.00

Time

1:

1:

1:

0.00

1.00

2.00

1: population1

1

1

1

1

population1: p1 (Unti tled)

Coupled GrowersEffects

Plot of changing coupling factorAnd output population1 and 2 ?!

For this STELLA is not suitedUSE MATLAB

MATLAB

• Some Experiments with Coupled Growers•

X n+1 = F(Xn;αX)+ε[F(Yn;αY )−F(Xn;αX),Y n+1 = F(Yn;αY )− ε[F(Yn;αY)−F(Xn;αX)].

Experiments with Coupled Growers(Savi 2007)

X n+1 = F(Xn;αX)+ε[F(Yn;αY )−F(Xn;αX),Y n+1 = F(Yn;αY )− ε[F(Yn;αY)−F(Xn;αX)].

Logistic map bifurcation diagram αX = 3.8 (chaos) and αY=2.5 (period 1)

ε

X n+1

Experiments with Coupled Growers(Savi 2007)

X n+1 = F(Xn;αX)+ε[F(Yn;αY )−F(Xn;αX),Y n+1 = F(Yn;αY )− ε[F(Yn;αY)−F(Xn;αX)].

Logistic map bifurcation diagram αX = 3.8 (chaos) and αY=2.5 (period 1)

ε

Yn+1

Some Literature

• Barlas, Y. 1989. “Multiple Tests for Validation of System Dynamics Type of Simulation Models.” European Journal of Operational Research 42(1):59-87.

• Dijkum C. van (2001). A Methodology for Conducting Interdisciplinary Social Research. European Journal of Operational Research,Vol.128,Iss. 2, 290-299.

• Dijkum C. van, Landsheer H. (2000). Experimenting with a Non-linear Dynamic Model of Juvenile Criminal Behavior. Simulation & Gaming, Vol.31, No.4, 479-490.

• Dijkum C. , Mens-Verhulst J. van, Kuijk E. van, Lam N. (2002), System Dynamic Experiments with Non-linearity and a Rate of Learning, Journal of Artificial Societies and Social Simulation, Vol. 5, 3.

• Dijkum, C. van, Verheul W. Bensing J., Lam N., Rooi J. de (2008). “Non Linear Models for the Feedback between GP and Patients.” In Cybernetics and Systems. Trappl R. (ed). Vienna: Austrian Society for Cybernetic Studies. (download: http://www.nosmo.nl/rc33/nonlinear.pdf)

• Forrester, J.W. (1968). Principles of Systems. Cambridge MA: Wright-Allen Press.

Some Literature

• Haefner J. W. (1996). Modeling biological systems. New York: Chapman & Hall.

• Hanneman, R.A (1988). Computer-assisted theory building: Modeling dynamic social systems. Newbury Park: Sage.

• Richardson, G.P. and A.L.Pugh III. 1981. Introduction To System Dynamics Modeling With DYNAMO. Portland, OR: Productivity Press.

• Schroots J., Dijkum C. van (2004). Autobiographical Memory Bump- A Dynamic Lifespan Model. Dynamical Psychology: An International, Interdisciplinary Journal of Complex Mental Processes. (http://www.goertzel.org/dynapsyc/dynacon.html)