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

Jaume Llibre; Feng Rong

doi: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

3 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
Volume	23
Issue number	2
DOIs	https://doi.org/10.1142/S0218127413500247
Publication status	Published - 1 Jan 2013

Keywords

averaging method
discontinuous piecewise linear differential systems
Limit cycles

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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.",

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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.

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KW - Limit cycles

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