Piecewise linear differential systems with an algebraic line of separation
We study the number of limit cycles of planar piecewise linear differential systems separated by a branch of an algebraic curve. We show that for each $n\in\mathbb{N}$ there exist piecewise linear differential systems separated by an algebraic curve of degree $n$ having [n/2] hyperbolic limit cy...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2020-02-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2020/19/abstr.html |
| Summary: | We study the number of limit cycles of planar piecewise linear differential
systems separated by a branch of an algebraic curve. We show that for each
$n\in\mathbb{N}$ there exist piecewise linear differential systems separated by
an algebraic curve of degree $n$ having [n/2] hyperbolic limit cycles.
Moreover, when n=2,3, we study in more detail the problem, considering
a perturbation of a center and constructing examples with 4 and 5 limit cycles,
respectively. These results follow by proving that the set of functions
generating the first order averaged function associated to the problem is an
extended complete Chebyshev system in a suitable interval. |
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| ISSN: | 1072-6691 |