On the number of limit cycles for discontinuous piecewise linear differential systems in ℝ2n with two zones

Jaume Llibre; Feng Rong

doi:https://doi.org/10.1142/S0218127413500247

On the number of limit cycles for discontinuous piecewise linear differential systems in ℝ²ⁿ with two zones

Jaume Llibre, Feng Rong

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

4 Citations (Scopus)

Abstract

We study the number of limit cycles of the discontinuous piecewise linear differential systems in ℝ2n with two zones separated by a hyperplane. Our main result shows that at most (8n - 6)n-1 limit cycles can bifurcate up to first-order expansion of the displacement function with respect to a small parameter. For proving this result, we use the averaging theory in a form where the differentiability of the system is not necessary. © 2013 World Scientific Publishing Company.

Original language	English
Article number	1350024
Journal	International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume	23
Issue number	2
DOIs	https://doi.org/10.1142/S0218127413500247
Publication status	Published - 1 Jan 2013

Keywords

Limit cycles
averaging method
discontinuous piecewise linear differential systems

Access to Document

https://doi.org/10.1142/S0218127413500247

https://ddd.uab.cat/record/150645

Cite this

@article{ecb6e215e433408bbfed5de84c0bd57d,

title = "On the number of limit cycles for discontinuous piecewise linear differential systems in ℝ2n with two zones",

abstract = "We study the number of limit cycles of the discontinuous piecewise linear differential systems in ℝ2n with two zones separated by a hyperplane. Our main result shows that at most (8n - 6)n-1 limit cycles can bifurcate up to first-order expansion of the displacement function with respect to a small parameter. For proving this result, we use the averaging theory in a form where the differentiability of the system is not necessary. {\textcopyright} 2013 World Scientific Publishing Company.",

keywords = "Limit cycles, averaging method, discontinuous piecewise linear differential systems",

author = "Jaume Llibre and Feng Rong",

year = "2013",

month = jan,

day = "1",

doi = "https://doi.org/10.1142/S0218127413500247",

language = "English",

volume = "23",

number = "2",

}

TY - JOUR

T1 - On the number of limit cycles for discontinuous piecewise linear differential systems in ℝ2n with two zones

AU - Llibre, Jaume

AU - Rong, Feng

PY - 2013/1/1

Y1 - 2013/1/1

N2 - We study the number of limit cycles of the discontinuous piecewise linear differential systems in ℝ2n with two zones separated by a hyperplane. Our main result shows that at most (8n - 6)n-1 limit cycles can bifurcate up to first-order expansion of the displacement function with respect to a small parameter. For proving this result, we use the averaging theory in a form where the differentiability of the system is not necessary. © 2013 World Scientific Publishing Company.

AB - We study the number of limit cycles of the discontinuous piecewise linear differential systems in ℝ2n with two zones separated by a hyperplane. Our main result shows that at most (8n - 6)n-1 limit cycles can bifurcate up to first-order expansion of the displacement function with respect to a small parameter. For proving this result, we use the averaging theory in a form where the differentiability of the system is not necessary. © 2013 World Scientific Publishing Company.

KW - Limit cycles

KW - averaging method

KW - discontinuous piecewise linear differential systems

U2 - https://doi.org/10.1142/S0218127413500247

DO - https://doi.org/10.1142/S0218127413500247

M3 - Article

VL - 23

IS - 2

M1 - 1350024