Limit cycles for rigid cubic systems

A. Gasull; Rafel Prohens; J. Torregrosa

doi:https://doi.org/10.1016/j.jmaa.2004.07.030

Limit cycles for rigid cubic systems

A. Gasull, Rafel Prohens, J. Torregrosa

Department of Mathematics

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

28 Citations (Scopus)

Abstract

We consider planar cubic systems with a unique rest point of center-focus type and constant angular velocity. For such systems we obtain an affine classification in three families, and, for two of them, their corresponding phase portraits on the Poincaré sphere. We also prove that for two of these families there is uniqueness of limit cycle. With respect the third family, we give the bifurcation diagram and phase portraits on the Poincaré sphere of a one-parameter sub-family exhibiting at least two limit cycles. © 2004 Elsevier Inc. All rights reserved.

Original language	English
Pages (from-to)	391-404
Journal	Journal of Mathematical Analysis and Applications
Volume	303
DOIs	https://doi.org/10.1016/j.jmaa.2004.07.030
Publication status	Published - 15 Mar 2005

Keywords

Bifurcation
Center
Cubic system
Limit cycle

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title = "Limit cycles for rigid cubic systems",

abstract = "We consider planar cubic systems with a unique rest point of center-focus type and constant angular velocity. For such systems we obtain an affine classification in three families, and, for two of them, their corresponding phase portraits on the Poincar{\'e} sphere. We also prove that for two of these families there is uniqueness of limit cycle. With respect the third family, we give the bifurcation diagram and phase portraits on the Poincar{\'e} sphere of a one-parameter sub-family exhibiting at least two limit cycles. {\textcopyright} 2004 Elsevier Inc. All rights reserved.",

keywords = "Bifurcation, Center, Cubic system, Limit cycle",

author = "A. Gasull and Rafel Prohens and J. Torregrosa",

year = "2005",

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doi = "https://doi.org/10.1016/j.jmaa.2004.07.030",

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TY - JOUR

T1 - Limit cycles for rigid cubic systems

AU - Gasull, A.

AU - Prohens, Rafel

AU - Torregrosa, J.

PY - 2005/3/15

Y1 - 2005/3/15

N2 - We consider planar cubic systems with a unique rest point of center-focus type and constant angular velocity. For such systems we obtain an affine classification in three families, and, for two of them, their corresponding phase portraits on the Poincaré sphere. We also prove that for two of these families there is uniqueness of limit cycle. With respect the third family, we give the bifurcation diagram and phase portraits on the Poincaré sphere of a one-parameter sub-family exhibiting at least two limit cycles. © 2004 Elsevier Inc. All rights reserved.

AB - We consider planar cubic systems with a unique rest point of center-focus type and constant angular velocity. For such systems we obtain an affine classification in three families, and, for two of them, their corresponding phase portraits on the Poincaré sphere. We also prove that for two of these families there is uniqueness of limit cycle. With respect the third family, we give the bifurcation diagram and phase portraits on the Poincaré sphere of a one-parameter sub-family exhibiting at least two limit cycles. © 2004 Elsevier Inc. All rights reserved.

KW - Bifurcation

KW - Center

KW - Cubic system

KW - Limit cycle

U2 - https://doi.org/10.1016/j.jmaa.2004.07.030

DO - https://doi.org/10.1016/j.jmaa.2004.07.030

M3 - Article

VL - 303

SP - 391

EP - 404

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

ER -