On the number of limit cycles in general planar piecewise linear systems of node–node types ☆

By Songmei Huan, Xiao-Song Yang. 2014

101 citations recorded by the source corpus.

Subfields: Biochemistry, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/3f8d31b7a45442ad72b102bfbf799479c50badb0

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In Biochemistry

In Geometry and Topology

In Statistical and Nonlinear Physics

Citations in the corpus

Uniqueness of limit cycles for sewing planar piecewise linear systems (2015, methodology): “The equivalent canonical form used in [14, 15, 20] can be obtained from the twin change of variables (u, v) = (−y, x − μ1 y) and (u, v) = (−y, x − μ1 y) in Σ±, respectively.”
Limit cycles for discontinuous planar piecewise linear differential systems separated by one straight line and having a center (2018, background): “Limit cycles of discontinuous piecewise linear differential systems separated by a straight line have been studied by many authors, see for instance [2, 8, 9, 11, 13, 14, 21, 26] and the references therein.”
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].”
On the number of limit cycles in discontinuous piecewise linear differential systems with two pieces separated by a straight line (2014, background): “n–sliding limit cycle. Limit cycles of discontinuous piecewise linear diﬀerential systems with two pieces separated by a straight line have been studied by many authors, see for instance the articles [2, 8, 9, 11, 13, 14, 15, 20, 21, 24]. Summarizing the results of these articles we have that the ma”
Three crossing limit cycles in planar piecewise linear systems with saddle-focus type (2014, background): “For this reason, many authors have contributed to develop several valid systematic methods in order to overcome the obstacles in recent years; for instance, see [1, 2, 6, 9, 11–14,16–18,22].”
Maximum number of limit cycles for certain piecewise linear dynamical systems (2015, background): “Of course, limit cycles of discontinuous piecewise linear differential systems with two zones separated by a straight line have been studied recently by several authors, see among others [2, 8, 10, 12, 14, 15, 17, 18, 19, 25, 26, 27, 28].”