### Liénard system

Let us consider the following Liénard system corresponding to a perturbation of a weak focus [Perko (2001)]:

\begin{equation*} \begin{cases} \dot{x} = y + \varepsilon p(x) \\ \dot{y} = -x, \end{cases} \end{equation*}
where the perturbation function $p$ is given by:
\begin{equation*} p(x) = 72 x - \dfrac{392}{3} x^3 + \dfrac{224}{5} x^5 - \dfrac{128}{35} x^7 . \end{equation*}
You can visualize the phase portrait of the perturbed system: choose a value of $10\varepsilon$ (decimal number between $0$ and $1$). For $\varepsilon > 0$ sufficiently small, the system presents 2 stable limit cycles and 1 unstable limit cycle.

### Simulation

$10 \varepsilon =$ You must enter a decimal number between $0$ and $1$.

Phase portrait of the Liénard system

## Bibliography

L. Perko. Differential equations and dynamical systems. Springer, New York, 3rd edition, 2001.