van_der_pol_trap

Scicos Diagram
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Discrete Van Der Pol's system (trapezoidal method)

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

The Van Der Pol's equation is :

$\begin{eqnarray} x+\left(x^{2}-1\right)\dot{x}+x=0 \end{eqnarray}$

It can be described by the following system of state equations :

$\begin{eqnarray} \dot{x}&=&y\\ \dot{y}&=&\left(1-x^{2}\right)y-x \end{eqnarray}$

Te   = 0.01
Tfin = 90
ci   = [-1;0]

$\begin{figure}\begin{center} \epsfig{file=van_der_pol_trap_scope_1.eps,width=330.00pt} \end{center}\end{figure}$

Figure : (a) Time domain waveforms of state variables

$\begin{figure}\begin{center} \epsfig{file=van_der_pol_trap_scope_2.eps,width=330.00pt} \end{center}\end{figure}$

Figure : (b) Phase plan

A. Layec