Scicos Diagram
eng - fr


Duffing's oscillator

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

Description

The Duffing's equation is described by this non-linear differential equation :

$\displaystyle \frac{y\left(t\right)}{dt}\,=\,x\left(t\right)-x^{3}\left(t\right)-\epsilon y\left(t\right)+\gamma\cos\left(\omega t\right)
$

where $ \epsilon$ and $ \gamma$ are parameters and $ \omega$ a pulsation.
This forced oscillator should be written as a three dimensional state equation system :

$\displaystyle \tilde{x_{1}}\,=\,x_{2}
$

$\displaystyle \tilde{x_{2}}\,=\,x_{1}-x_{1}^{3}-\epsilon y+\gamma\cos\left(x_{3}\right)
$

$\displaystyle \tilde{x_{3}}\,=\,\frac{2\pi}{T}
$

Context


Te=0.02
Tfin=200
g=0.3
a=0.15
w=1
To=2*%pi/w
ci1=0.1
ci2=0.1
ci3=0
 

Scope Results

\begin{figure}\begin{center}
\epsfig{file=duffing_scope_1.eps,width=300.00pt}
\end{center}\end{figure}
Figure : (a) Time domain wave forms
\begin{figure}\begin{center}
\epsfig{file=duffing_scope_2.eps,width=300.00pt}
\end{center}\end{figure}
Figure : (b) Phase plan
\begin{figure}\begin{center}
\epsfig{file=duffing_scope_3.eps,width=300.00pt}
\end{center}\end{figure}
Figure : (c) Poincare section

Authors

IRCOM Group Alan Layec