Scicos Diagram
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Chua's system

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Description

This system takes an important place in the understanding of the synchronization of chaotic systems. He is originally studed with the electronic circuit shown in the following Figure. This circuit is composed with passive elements and with an active non-linear element.

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Figure : Chua's circuit

This circuit is described by the following state equations:

$\displaystyle \frac{dV_{1}}{dt}\,=\,\frac{1}{C_{1}}\left[\frac{1}{R}\left(V_{2}-V_{1}\right)-i_{NL}\right]
$

$\displaystyle \frac{dV_{2}}{dt}\,=\,\frac{1}{C_{2}}\left[i_{l}-\frac{1}{R}\left(V_{2}-V_{1}\right)\right] \nonumber
$

$\displaystyle \frac{di_{l}}{dt}\,=\,-\frac{1}{L}V_{2} \nonumber
$

$\displaystyle f(V_{1})\,=\,G_{b}\, V_{1}+\frac{1}{2}\left[G_{a}-G_{b}\right]\, \left[\left\vert V_{1}+E\right\vert-\left\vert V_{1}-E\right\vert\right]
$

By changing parameters with $ \alpha=\dfrac{C_{2}}{C_{1}}$, $ \beta=\dfrac{C_{2}}{L}R^{2}$, $ m_{0}=\dfrac{G_{a}}{R}$, $ m_{1}=\dfrac{G_{b}}{R}$and renamming state variables, the new sate equations are:

$\displaystyle \tilde{x}_{1}\,=\,\alpha\left[x_{2}-x_{1}-h\left(x_{1}\right)\right]
$

$\displaystyle \tilde{x}_{2}\,=\,x_{3}-x_{2}-x_{1} \nonumber
$

$\displaystyle \tilde{x}_{3}\,=\,-\beta x_{2} \nonumber
$

$\displaystyle h(x)\,=\,m_{1}\, x+\frac{1}{2}\left[m_{0}-m_{1}\right]\, \left[\left\vert x+E\right\vert-\left\vert x-E\right\vert\right]
$

Context


Tsampl = 1e-2
Tfin = 60
m0=-8/7
m1=-5/7
ci=[1.6;0;-1.6]

Scope Results

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Figure : (a) Temporal wave forms of state variables
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Figure : (b) Phase plan

Mod_num blocks

See Also

Authors

IRCOM Group Alan Layec