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# Lienard system

A *Lienard system* is a planar ordinary differential equation

$\displaystyle\dot{x}$ | $\displaystyle=$ | $\displaystyle y-f(x)$ | ||

$\displaystyle\dot{y}$ | $\displaystyle=$ | $\displaystyle-g(x)$ |

with conditions on the smoothness of $f$ and $g$. It is equivalent to the following second order ordinary differential equation

$\ddot{x}+f^{{\prime}}(x)\dot{x}+g(x)=0.$ |

Example:

# References

- P
Perko, Lawrence,
*Differential Equations and Dynamical Systems*, Springer, New York, 2001.

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Lienard equation

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