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 x' = y−F(x)+p(ωt), 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.
Chaotic dynamics in a periodically perturbed Liénard system / Papini, D.; Villari, G.; Zanolin, F.. - In: DIFFERENTIAL AND INTEGRAL EQUATIONS. - ISSN 0893-4983. - 32:11-12(2019), pp. 595-614.
Chaotic dynamics in a periodically perturbed Liénard system
Papini D.;
2019
Abstract
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 x' = y−F(x)+p(ωt), 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.
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