Download 4.2. Installing Microsoft Visual Studio 2003

EcosimPro 4.8
direction for a bit, then slows down and starts to spin in the other. The waterwheel will constantly change its
direction of spin, and never in a repeating predictable manner. Here is a picture of the waterwheel. Many more
sophisticated but similar systems have been built, and they all show the same chaotic behaviour.
Lorentz equations are actually three differential equations, a first order equation for each of the y1, y2 and y3
components of the trajectory position. They are given as:
y1' = alfa*(y2 - y1)
y2' = r*y1 - y2 - y1*y3
y3' = y1*y2 - b*y3
where r, b and alfa are parameters that change the behaviour of the system. There are a lot of resources available if
you wish to study the Lorentz equations in detail. These equations are usually the first chaotic differential equations
introduced in any book on chaos. Ed Lorentz' paper (1963) is also a very good source of information.
An component modelling the equations is listed below, and the default experiment can be run in the DEFALT_LIB
library, as in previous examples.
COMPONENT Lorentz
DATA
REAL alfa = 10
REAL b = 8/3
REAL r = 28
DECLS
REAL y1 = 0
REAL y2 = 1
REAL y3 = 0
CONTINUOUS
y1' = alfa*(y2 - y1)
y2' = r*y1 - y2 - y1*y3
y3' = y1*y2 - b*y3
END COMPONENT
The following graphic shows the evolution of the solution in the XZ plane, but similar graphics could be obtained in
other planes.
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