Lienard system

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

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.