Differential and Integral Equations

Chaotic dynamics in a periodically perturbed Liénard system

Duccio Papini, Gabriele Villari, and Fabio Zanolin

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We prove the existence of infinitely many periodic solutions, as well as the presence of chaotic dynamics, for a periodically perturbed planar Liénard system of the form $\dot{x} = y - F(x) + p(\omega t),\; \dot{y} = - g(x)$. We consider the case in which the perturbing term is not necessarily small. Such a result is achieved by a topological method, that is by proving the presence of a horseshoe structure.

Article information

Differential Integral Equations, Volume 32, Number 11/12 (2019), 595-614.

First available in Project Euclid: 22 October 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 34C05: Location of integral curves, singular points, limit cycles 34C25: Periodic solutions 34C15: Nonlinear oscillations, coupled oscillators


Papini, Duccio; Villari, Gabriele; Zanolin, Fabio. Chaotic dynamics in a periodically perturbed Liénard system. Differential Integral Equations 32 (2019), no. 11/12, 595--614. https://projecteuclid.org/euclid.die/1571731511

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