Piecewise linear perturbations of a linear center

By Claudio Aguinaldo Buzzi, Claudio Pessoa, Joan Torregrosa. 2013

162 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/425e0ccebc9711265166da41768820ea3fa239f1

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In Geometry and Topology

Citations in the corpus

Averaging theory at any order for computing limit cycles of discontinuous piecewise differential systems with many zones (2016, background): “The bifurcation of limit cycles from smooth and nonsmooth perturbations of the linear center (ẋ, ẏ) = (−y, x) is a fairly studied problem in the literature, see for instance [3, 4, 9, 18, 19].”
Limit cycles for discontinuous planar piecewise linear differential systems separated by one straight line and having a center (2018, background): “There are examples of such systems exhibiting three limit cycles, see [5, 6, 10, 12, 17, 20], and at this moment we do not know if discontinuous piecewise linear differential systems separated by a straight line can have more than three limit cycles.”
The pseudo-Hopf bifurcation for planar discontinuous piecewise linear differential systems (2017, background): “In the discontinuous ones we can have more than one limit cycle, either all crossing cycles or including one sliding cycle, and in fact, the determination of the number of limit cycle has been the subject of several recent papers, see [2, 3, 4, 10, 15, 16, 17, 20, 22, 23, 24].”
Bifurcation of limit cycles at infinity in piecewise polynomial systems (2018, background): “[23] studied the limit cycles that bifurcate from a linear center using a piecewise linear perturbation in two zones.”
Limit cycles in planar piecewise linear differential systems with nonregular separation line (2016, methodology): “The existence of other examples with three limit cycles, via bifurcation techniques, can be found in [5, 13].”
Piecewise linear differential systems with only centers can create limit cycles? (2017, background): “It is known that such systems can have three limit cycles, see [4,5,9,11,14,16].”
Uniqueness of limit cycles for sewing planar piecewise linear systems (2015, background): “Recently, examples of piecewise linear systems with a sliding segment that present two and three limit cycles are provided, see among others [3, 13, 14, 15] and [5, 7, 19], respectively.”