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liénard's
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Periodic solutions of Liénard's' equation - ScienceDirect. ScienceDirect.
Please enable JavaScript to use all the features on this page. Skip to main content Skip to article. Register Sign in. Download full issue. Journal of Mathematical Analysis and Applications. Volume 86, Issue 2, April 1982, Pages 379-386. Periodic solutions of Liénard's' equation.
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Van der Pol oscillator - Scholarpedia.
When x is small, the quadratic term x2 is negligible and the systembecomes a linear differential equation with a negative damping - epsilon dot x Thus, the fixed point x0, dot x 0, is un stable an unstable focus when 0 epsilon 2 and an unstable node, otherwise .On the other hand, when x is large, the term x2 becomes dominantand the damping becomes positive.Therefore, the dynamics of the system is expected to be restrictedin some area around the fixed point.Actually, the van der Pol system 1 satisfies the Liénard's' theorem ensuring that there is a stable limit cycle in the phase space The van der Pol system is therefore a Liénard system.
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LIÉNARD SYSTEMS.
A great number of mathematical models of physical systems give riseto differential equations of the type. This is known as Liénard's' equation. The system is a generalizationof the mass-spring-damper system. In Liénard's' equation isthe damping term and isthe spring term.
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Liénard equation - Wikipedia.
In mathematics, more specifically in the study of dynamical systems and differential equations, a Liénard equation 1 is a second order 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.
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