Scicos Diagram
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Lorentz equation

\epsfig{file=Lorentz_diagr.eps,width=400pt}

Module


Contents

Description

The Lorentz's system is defined by the following continuous system :

\begin{eqnarray}
\frac{dx(t)}{dt}&=&a\left(-x(t)+y(t)\right)\\
\frac{dy(t)}{dt}&=&bx(t)-y(t)-x(t)y(t)\\
\frac{dz(t)}{dt}&=&-cx(t)+x(t)y(t)
\end{eqnarray}


The state variables $ x(t)$, $ y(t)$ and $ z(t)$ are respectively temperature of the air, speed of wind and a third variable which represents the variation of temperature according to the altitude.

Context


//set sampling time
Tsampl=3e-3

//set parameters
a=10
b=28
c=8/3

//set initial conditions
ci1=[5.5;5.49;5.51;5.511]
ci2=[5;4.99;5.01;5.011]
ci3=[20;19.99;20.01;20.011]

//set colors for scopes
vcol=[0;3;5;9]

//set end simulation time
Tfin=30

Scope Results

\begin{figure}\begin{center}
\epsfig{file=Lorentz_scope_1.eps,width=330.00pt}
\end{center}\end{figure}
Figure : (a) Time domain waveforms of state variables (x,y,z)
\begin{figure}\begin{center}
\epsfig{file=Lorentz_scope_2.eps,width=330.00pt}
\end{center}\end{figure}
Figure : (b) Trajectories in the phase plan (x,y,z)
\begin{figure}\begin{center}
\epsfig{file=Lorentz_scope_3.eps,width=330.00pt}
\end{center}\end{figure}
Figure : Scope results

Used blocks

Authors

Alan Layec INRIA