Modeling chaos 3

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Modeling chaos 3
2
Chaos in continuous systems
3
Rossler differential equation
Parametrs a0.2, b0.2
4
Periodic solutions
5
c2.5
6
c3.5
7
c4.0
8
Rossler attractor c5.7
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Mechanism of period doubling Defining and
analysis of Poincare map
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xn1
xn
8
6
4
2
0
y
-2
-4
-6
-8
-10
-12
-10
-5
0
5
10
15
x
11
y
12
0
x
z
-4
12
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12
10
8
n1
6
x
4
2
0
0
2
4
6
8
10
12
x
n
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Bifurcation diagram for Rossler equation
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Lorenz equation
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Model for fluid motion due to temperature gradient
?T
17

• Fluid moves along level surfaces

Iostherms
Parameters
18
Periodic solution
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Chaotic solution