Cyclicity of (1,3)-switching FF type equilibria

Xingwu Chen; Jaume Llibre; Weinian Zhang

doi:https://doi.org/10.3934/dcdsb.2019153

Cyclicity of (1,3)-switching FF type equilibria

Xingwu Chen, Jaume Llibre, Weinian Zhang

Department of Mathematics

Research output: Contribution to journal › Article › Research

Abstract

© 2019 American Institute of Mathematical Sciences. All rights reserved. Hilbert’s 16th Problem suggests a concern to the cyclicity of planar polynomial differential systems, but it is known that a key step to the answer is finding the cyclicity of center-focus equilibria of polynomial differential systems (even of order 2 or 3). Correspondingly, the same question for polynomial discontinuous differential systems is also interesting. Recently, it was proved that the cyclicity of (1, 2)-switching FF type equilibria is at least 5. In this paper we prove that the cyclicity of (1, 3)-switching FF type equilibria with homogeneous cubic nonlinearities is at least 3.

Original language	English
Pages (from-to)	6541-6552
Journal	Discrete and Continuous Dynamical Systems - Series B
Volume	24
DOIs	https://doi.org/10.3934/dcdsb.2019153
Publication status	Published - 1 Dec 2019

Keywords

Cyclicity
Discontinuous differential system
Hopf bifurcation
Limit cycle

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title = "Cyclicity of (1,3)-switching FF type equilibria",

abstract = "{\textcopyright} 2019 American Institute of Mathematical Sciences. All rights reserved. Hilbert{\textquoteright}s 16th Problem suggests a concern to the cyclicity of planar polynomial differential systems, but it is known that a key step to the answer is finding the cyclicity of center-focus equilibria of polynomial differential systems (even of order 2 or 3). Correspondingly, the same question for polynomial discontinuous differential systems is also interesting. Recently, it was proved that the cyclicity of (1, 2)-switching FF type equilibria is at least 5. In this paper we prove that the cyclicity of (1, 3)-switching FF type equilibria with homogeneous cubic nonlinearities is at least 3.",

keywords = "Cyclicity, Discontinuous differential system, Hopf bifurcation, Limit cycle",

author = "Xingwu Chen and Jaume Llibre and Weinian Zhang",

year = "2019",

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doi = "https://doi.org/10.3934/dcdsb.2019153",

language = "English",

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journal = "Discrete and Continuous Dynamical Systems - Series B",

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T1 - Cyclicity of (1,3)-switching FF type equilibria

AU - Chen, Xingwu

AU - Llibre, Jaume

AU - Zhang, Weinian

PY - 2019/12/1

Y1 - 2019/12/1

N2 - © 2019 American Institute of Mathematical Sciences. All rights reserved. Hilbert’s 16th Problem suggests a concern to the cyclicity of planar polynomial differential systems, but it is known that a key step to the answer is finding the cyclicity of center-focus equilibria of polynomial differential systems (even of order 2 or 3). Correspondingly, the same question for polynomial discontinuous differential systems is also interesting. Recently, it was proved that the cyclicity of (1, 2)-switching FF type equilibria is at least 5. In this paper we prove that the cyclicity of (1, 3)-switching FF type equilibria with homogeneous cubic nonlinearities is at least 3.

AB - © 2019 American Institute of Mathematical Sciences. All rights reserved. Hilbert’s 16th Problem suggests a concern to the cyclicity of planar polynomial differential systems, but it is known that a key step to the answer is finding the cyclicity of center-focus equilibria of polynomial differential systems (even of order 2 or 3). Correspondingly, the same question for polynomial discontinuous differential systems is also interesting. Recently, it was proved that the cyclicity of (1, 2)-switching FF type equilibria is at least 5. In this paper we prove that the cyclicity of (1, 3)-switching FF type equilibria with homogeneous cubic nonlinearities is at least 3.

KW - Cyclicity

KW - Discontinuous differential system

KW - Hopf bifurcation

KW - Limit cycle

UR - https://ddd.uab.cat/record/221339

U2 - https://doi.org/10.3934/dcdsb.2019153

DO - https://doi.org/10.3934/dcdsb.2019153

M3 - Article

VL - 24

SP - 6541

EP - 6552

JO - Discrete and Continuous Dynamical Systems - Series B

JF - Discrete and Continuous Dynamical Systems - Series B

SN - 1531-3492

ER -