Liénard equation

In mathematics, more specifically in the study of dynamical systems and differential equations, a Liénard equation is a type of second-order ordinary differential equation named after the French physicist Alfred-Marie Liénard.

During the development of radio and vacuum tube technology, Liénard equations were intensely studied as they can be used to model oscillating circuits. Under certain additional assumptions Liénard's theorem guarantees the uniqueness and existence of a limit cycle for such a system. A Liénard system with piecewise-linear functions can also contain homoclinic orbits.