# 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

Title Lienard system LienardSystem 2013-03-22 15:20:45 2013-03-22 15:20:45 Daume (40) Daume (40) 6 Daume (40) Definition msc 34-00 Lienard equation