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Discrete forced Van Der Pol's system (Euler method)

Module

• Modnum

Contents

• Discrete forced Van Der Pol's system (Euler method)
  • Module
  • Description
  • Context
  • Scope Results
  • Used blocks
  • See Also
  • Authors

Description

This system do the illustration of the use of a single step integrator in order to solve a continuous system.
Here the system is solved with the backward Euler method. The forced Van Der Pol's oscillator is described with this system of state equation :

$$\begin{eqnarray} \dot{x}&=&y\\ \dot{y}&=&\left(1-x^{2}\right)y-x+A\cos\left(z\right)\\ \dot{z}&=&\frac{2\pi}{T} \end{eqnarray}$$

where parameters $T$ is the period of the driven oscillator and $A$ its amplitude.

Context

Te   = 0.01
ci   = [-1;0]
A    = 0.5;
wo   = 1.1;
To   = 2*%pi/wo;
Tfin = 90

Scope Results

Figure : (a) Time domain waveforms of state variables

Figure : (b) Phase plan

Used blocks

• EULERINTEGRAL_m - Single step integrator block by Euler method

See Also

• EULERINTEGRAL_f - Single step integrator block by Euler method (old block) (Scicos Block)

Authors

A. Layec