chaos and system dynamics
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Chaos and System dynamics. Leon Chang. Edward Lorenz. - PowerPoint PPT PresentationTRANSCRIPT
Chaos and System dynamics
Leon Chang
Edward Lorenz
In the early 1960's using a simple
system of equations to model con
vection in the atmosphere, Edwar
d Lorenz, an MIT meteorologist,
ran headlong into "sensitivity to i
nitial conditions". In the process
he sketched the outlines of one of
the first recognized chaotic attract
ors.
The Butterfly Effect
The "Butterfly Effect" is the propensity of a system to be sensitive to initial conditions.Such systems over time become unpredictable,this idea gave rise to the notion of a butterfly flapping it's wings in one area of the world,causing a tornado or some such weather event to occur in another remote area of the world
Lorenz model
bzxyz
yrxxzy
yxx
H ot
C ool
Lorenz waterwheel
Lorenz model by system dynamicsX
dXdt
Z
Y
dZdt
dYdt
S
B
RminusZ
R
bzxyz
yrxxzy
yxx
Lorenz result
10:13 PM 2004¦~4¤ë3¤é
1.00 13.25 25.50 37.75 50.00
Months
1:
1:
1:
-25.00
5.00
35.00
1: Y
1
1
1
1
Graph 1 (Untitled)
r=28.00
03:41 PM 2004¦~4¤ë4¤é
1.00 13.25 25.50 37.75 50.00
Months
1:
1:
1:
-30.00
0.00
30.00
1: Y 2: Y 3: Y
1
1
1
1
22
2
2
3
3
33
Graph 1 (Untitled)
1: r=28.002: r=28.013: r=28.03
Lorenz result comparison
Strange attractor by X-Y
10:18 PM 2004¦~4¤ë3¤éX
-25.00 0.00 25.00-25.00
5.00
35.00
1: X v. Y
Graph 1 (Untitled)
08:54 PM 2004¦~4¤ë4¤éZ
5.00 30.00 55.00-25.00
5.00
35.00
1: Z v. Y
Graph 1 (Untitled)
Strange attractor by Y-Z
10:25 PM 2004¦~4¤ë3¤éX
-25.00 0.00 25.00-250.00
0.00
250.00
1-2: X v. dXdt
Graph 1 (Untitled)
Strange attractor by X-dX/dt
Lorenz attractor
成長上限
銷售能力和規模
訂單數量
營業收入
欠貨數量
交貨期
銷售困難度
+
++
+
+
-
+
+
++ -
成本與投資不足
成長的行動
需求
績效
認知的投資需求
產能
產能的投資
+ -
-
Using system dynamics to analyse interactions in duopoly competitionPetia Sicea, Erik Mosekildeb, Alfredo Moscardinic, Kevin Lawlerc and Ian Frenchd*System Dynamics Review Vol. 16, No. 2, (Summer 2000): 113–133
Phase planeportrait (FQ against CQ)illustrating the singleperiodlimit cyclebehaviour observed fora = 2 and c = 0.1
Phase planeportrait (FQ against CQ)illustrating the chaoticbehaviour for a = 2 andc = 0.4
Plot of D overthe period 750 to 7000months; the straightline, which has slope0.005, represents the‘best fit’ over theperiod 1500 to 4500
Fractal