Generic bifurcations of low codimension of planar Filippov Systems

By Marcel Guardia, Tere M. Seara, Marco Antonio Teixeira. 2011

332 citations recorded by the source corpus.

Abstract In this article some qualitative and geometric aspects of non-smooth dynamical systems theory are discussed. The main aim of this article is to develop a systematic method for studying local (and global) bifurcations in non-smooth dynamical systems. Our results deal with the classification and characterization of generic codimension-2 singularities of planar Filippov Systems as well as the presentation of the bifurcation diagrams and some dynamical consequences.

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

View Paper: https://www.semanticscholar.org/paper/1db2c1a942b2a4f7a8f72dde4b05e49f5e868034

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In Astronomy and Astrophysics

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Citations in the corpus

Birth of limit cycles bifurcating from a nonsmooth center (2014, unknown): “Several recent papers [2, 3, 14, 15] describe the dynamics around typical singularities of certain parameterized families of planar PSVFs by means of the analysis of the correspondent bifurcation diagram.”
Dynamics and bifurcations of nonsmooth systems: A survey (2012, methodology): “We refer the reader to the aforementioned papers Guardia-Seara-Teixeira [154] and KuznetsovRinaldi-Gragnani [223] for classification of these points in R2.”
The pseudo-Hopf bifurcation for planar discontinuous piecewise linear differential systems (2017, background): “There are analogous results for piecewise smooth systems, for the case of continuous systems see for example [6, 7, 26, 27], and for the case of discontinuous systems see [1, 8, 11, 12, 14, 18].”
On Poincar\'e-Bendixson Theorem and Non-Trivial Minimal Sets in Planar Nonsmooth Vector Fields (2013, background): “In the literature there are several recent papers (see for instance [4, 5, 8, 10]) where the authors explicitly exhibit the phase portraits of some NSVFs with their unfoldings.”
Averaging theory at any order for computing limit cycles of discontinuous piecewise differential systems with many zones (2016, background): “For more details on the Filippov conventions see [8, 10].”
Bifurcations of piecewise smooth flows: Perspectives, methodologies and open problems (2012, background): “21 and 25; these also are not discussed generally in a forthcoming paper [89], but a case similar to the ‘simple canard’ in Fig.”