On the birth of limit cycles for non-smooth dynamical systems

By Jaume Llibre, Douglas Duarte Novaes, Marco Antonio Teixeira. 2012

137 citations recorded by the source corpus.

Abstract The main objective of this work is to develop, via Brower degree theory and regularization theory, a variation of the classical averaging method for detecting limit cycles of certain piecewise continuous dynamical systems. In fact, overall results are presented to ensure the existence of limit cycles of such systems. These results may represent new insights in averaging, in particular its relation with non-smooth dynamical systems theory. An application is presented in careful detail.

Subfields: Astronomy and Astrophysics, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/2466cfd63ef938d422180d9e9b74cc17c315b5bf

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In Astronomy and Astrophysics

In Geometry and Topology

In Statistical and Nonlinear Physics

Citations in the corpus

Averaging theory at any order for computing limit cycles of discontinuous piecewise differential systems with many zones (2016, background): “The extension of the averaging theory to discontinuous piecewise vector field has been the central subject of investigation of the following works [11, 12, 14, 17].”
A new result on averaging theory for a class of discontinuous planar differential systems with applications (2017, methodology): “For instance in [17], applying the theory of regularization, the averaging theory is extended up to order 1 for studying the”
On the maximum number of periodic solutions of piecewise smooth periodic equations by average method (2017, methodology): “Recently, the method has been developed from smooth differential equations to piecewise smooth differential equations, see [5, 6].”