One-Parameter bifurcations in Planar Filippov Systems

By Y. Kuznetsov, Sergio Rinaldi, Alessandra Gragnani. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 2003

626 citations recorded by the source corpus.

Subfields: Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/27920b2a4d97f323716801aecae8463cb052c63a

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Citations in the corpus

Numerical sliding bifurcation analysis: an application to a relay control system (2003, background): “As first pointed out by Filippov, these points (called tangent points in [17]), at which one of the two vectors is tangent to , are strategically important for bifurcation analysis.”
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.”
The pseudo-Hopf bifurcation for planar discontinuous piecewise linear differential systems (2017, background): “For the case of the invisible fold-fold singularity, when the vectors f−(q0) and f(q0) are antiparallel with q0 ∈ ∂Σc, the singularity is called fused-focus in [18].”
Birth of limit cycles bifurcating from a nonsmooth center (2014, neutral): “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.”
Bifurcations in Nonsmooth Dynamical Systems (2008, methodology): “An overview of local phenomena in planar Filippov systems was presented in [70].”
A Filippov sliding vector field on an attracting co-dimension 2 discontinuity surface, and a limited loss-of-attractivity analysis☆ (2013, background): “[4,5,13,22]; for works on the class of complementarity systems, see [14], for works from the point of view of bifurcations of dynamical-systems see [7,16,15,19]; and, of course, see the classical references [3,11,26,27] for a thorough theoretical introduction to these systems.”
Global analysis of a Holling type II predator–prey model with a constant prey refuge (2014, methodology): “Recently, discontinuous dynamic systems or Filippov systems have been widely used in many fields of science and engineering [1, 3, 7–10, 21, 28, 30, 31, 33].”