On the number of limit cycles in discontinuous piecewise linear differential systems with two pieces separated by a straight line
By Rodrigo D. Euz'ebio, Jaume Llibre. 2014
65 citations recorded by the source corpus.
Abstract In this paper we study the maximum number N of limit cycles that can exhibit a planar piecewise linear differential system formed by two pieces separated by a straight line. More precisely, we prove that this maximum number satisfies 2 ≤ N ≤ 4 if one of the two linear differential systems has its equilibrium point on the straight line of discontinuity.
Subfields: Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/8878f18c87c7ac0fe27d946f3efa37ea3dbafcbc
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In Geometry and Topology
- Xiang Zhang
- Jaume Llibre
- Joan Torregrosa
- Pedro Toniol Cardin
- Juan Castillo
- Fernando Verduzco
- Maite Grau
- Douglas Duarte Novaes
Citations in the corpus
- 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].”
- Limit cycles for discontinuous planar piecewise linear differential systems separated by one straight line and having a center (2018, background): “In the papers [8, 19, 18] it is proved that if one of the two linear differential systems has its equilibrium on the line of discontinuity, then the discontinuous piecewise linear differential system with two pieces separated by a straight line has at most 2 limit cycles.”
- Limit cycles in planar piecewise linear differential systems with nonregular separation line (2016, background): “In this case, Euzébio and Llibre in [9] proved that if one of the linear differential systems has its equilibrium point on the straight line of separation, then the maximum number is less or equal than four.”