THREE NESTED LIMIT CYCLES IN DISCONTINUOUS PIECEWISE LINEAR DIFFERENTIAL SYSTEMS WITH TWO ZONES

By Jaume Llibre, Enrique Ponce. 2012

163 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/46d326c766e67db28c10796fcba5914c1be3bad1

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Citations in the corpus

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].”
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.”
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.”
Limit cycles for discontinuous quadratic differential systems with two zones (2014, background): “Stimulated by discontinuous phenomena in the real world (see for instance the book [2] and the references quoted therein), a big interest has appeared for studying the limit cycles of discontinuous differential systems, mainly for discontinuous piecewise linear differential systems, see also the pap”
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].”
On the number of limit cycles in discontinuous piecewise linear differential systems with two pieces separated by a straight line (2014, background): “Llibre and Ponce in [20] inspired in the numerical example of [13] proved that there are discontinuous piecewise linear differential systems with two pieces separated by a straight line having three limit cycles.”
The discontinuous matching of two planar linear foci can have three nested crossing limit cycles (2014, background): “Recently, a computer assisted proof has been available, see [15], and based on such a proof it is shown in [2] that the three limit cycles can be obtained through a boundary focus bifurcation.”
On the birth of limit cycles for non-smooth dynamical systems (2012, methodology): “In [19] it is proved that the discontinuous differential equation (8) has three limit cycles (i) and that the their points (r0, θ0) and (r1, θ1) are approximately for the inner limit cycle of Figure 1”