Planar systems of piecewise linear differential equations with a line of discontinuity

By F. Giannakopoulos, Karin Pliete. 2001

171 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/c8c121539ce2622ec86230acad903f709e68e6e3

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In Control and Systems Engineering

In Geometry and Topology

In Statistical and Nonlinear Physics

Citations in the corpus

On the existence and uniqueness of limit cycles in planar continuous piecewise linear systems without symmetry (2013, background): “In a further step, other authors have considered a line of discontinuity in the vector field defining the planar system, see [14, 30].”
Three crossing limit cycles in planar piecewise linear systems with saddle-focus type (2014, unknown): “2010 Mathematics Subject Classification: 34A36, 34C05, 34C23, 37G05.”
Piecewise linear perturbations of a linear center (2013, background): “Limit cycles of discontinuous piecewise linear differential systems defined on two half-planes separated by a straight line have been studied recently in [5, 16, 17, 18, 21, 22], among other papers.”
Bifurcations in Nonsmooth Dynamical Systems (2008, methodology): “The transition to sliding cycles (a cycle with a segment of sliding motion) in planar Filippov systems is studied in [57].”
Bifurcation and chaos near sliding homoclinics (2010, background): “Many non-smooth models can be found in [1,2, 4,9,19,21,31,32,36,43–45].”
On the number of limit cycles in discontinuous piecewise linear differential systems with two pieces separated by a straight line (2014, methodology): “Now we recall the definitions of sliding segment and non–sliding limit cycle, for more details on these definitions see for instance [10] and [26].”
Limit cycles in planar piecewise linear differential systems with nonregular separation line (2016, background): “The question is: Which is the maximum number of isolated periodic orbits, also called limit cycles, that bifurcate perturbing a center? This problem for piecewise differential systems defined in two zones have been studied recently, among other papers, in [5, 7, 17, 18, 19, 22, 25, 26, 32].”