Stability of certain planar unbounded polycycles

Armengol Gasull; Víctor Mañosa; Francesc Mañosas

doi:10.1016/S0022-247X(02)00027-6

Stability of certain planar unbounded polycycles

Armengol Gasull, Víctor Mañosa, Francesc Mañosas

Department of Mathematics

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

4 Citations (Scopus)

Abstract

We study the stability of a type of unbounded polycycles which appear in some planar differential equations. Each of these polycycles has hyperbolic corners, but the product of the hyperbolicity ratios of all its corners does not decide its stability. We obtain an explicit convergent integral whose sign gives the stability of the polycycle. © 2002 Elsevier Science (USA). All rights reserved.

Original language	English
Pages (from-to)	332-351
Journal	Journal of Mathematical Analysis and Applications
Volume	269
Issue number	1
DOIs	https://doi.org/10.1016/S0022-247X(02)00027-6
Publication status	Published - 1 May 2002

Keywords

Bifurcation of limit cycles
Polycycle
Polynomial vector field
Stability

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title = "Stability of certain planar unbounded polycycles",

abstract = "We study the stability of a type of unbounded polycycles which appear in some planar differential equations. Each of these polycycles has hyperbolic corners, but the product of the hyperbolicity ratios of all its corners does not decide its stability. We obtain an explicit convergent integral whose sign gives the stability of the polycycle. {\textcopyright} 2002 Elsevier Science (USA). All rights reserved.",

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AU - Gasull, Armengol

AU - Mañosa, Víctor

AU - Mañosas, Francesc

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N2 - We study the stability of a type of unbounded polycycles which appear in some planar differential equations. Each of these polycycles has hyperbolic corners, but the product of the hyperbolicity ratios of all its corners does not decide its stability. We obtain an explicit convergent integral whose sign gives the stability of the polycycle. © 2002 Elsevier Science (USA). All rights reserved.

AB - We study the stability of a type of unbounded polycycles which appear in some planar differential equations. Each of these polycycles has hyperbolic corners, but the product of the hyperbolicity ratios of all its corners does not decide its stability. We obtain an explicit convergent integral whose sign gives the stability of the polycycle. © 2002 Elsevier Science (USA). All rights reserved.

KW - Bifurcation of limit cycles

KW - Polycycle

KW - Polynomial vector field

KW - Stability

U2 - 10.1016/S0022-247X(02)00027-6

DO - 10.1016/S0022-247X(02)00027-6

M3 - Article

VL - 269

SP - 332

EP - 351

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 1

ER -