PlanetMath: Lienard system

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Lienard system

(Definition)

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

with conditions on the smoothness of

and

. It is equivalent to the following second order ordinary differential equation

$\displaystyle \ddot{x}+f'(x)\dot{x}+g(x)=0.$

Example:

References

P: PERKO, LAWRENCE, Differential Equations and Dynamical Systems, Springer, New York, 2001.

"Lienard system" is owned by Daume.

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Also defines:

Lienard equation

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Cross-references: van der Pol equation, second order, ordinary differential equation, planar
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This is version 3 of Lienard system, born on 2005-06-18, modified 2006-07-27.
Object id is 7166, canonical name is LienardSystem.
Accessed 3468 times total.

Classification:

34-00 (Ordinary differential equations :: General reference works )

Pending Errata and Addenda

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