Exact number of limit cycles for a family of rigid systems

A. Gasull; J. Torregrosa

doi:https://doi.org/10.1090/S0002-9939-04-07542-2

Exact number of limit cycles for a family of rigid systems

A. Gasull, J. Torregrosa

Department of Mathematics

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

13 Citations (Scopus)

Abstract

For a given family of planar differential equations it is a very difficult problem to determine an upper bound for the number of its limit cycles. Even when this upper bound is one it is not always an easy problem to distinguish between the case of zero and one limit cycle. This note mainly deals with this second problem for a family of systems with a homogeneous nonlinear part. While the condition that allows us to separate the existence and the nonexistence of limit cycles can be described, it is very intricate. © 2004 American Mathematical Society.

Original language	English
Pages (from-to)	751-758
Journal	Proceedings of the American Mathematical Society
Volume	133
DOIs	https://doi.org/10.1090/S0002-9939-04-07542-2
Publication status	Published - 1 Mar 2005

Keywords

Bifurcation
Limit cycle
Rigid system
Rotated vector field

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abstract = "For a given family of planar differential equations it is a very difficult problem to determine an upper bound for the number of its limit cycles. Even when this upper bound is one it is not always an easy problem to distinguish between the case of zero and one limit cycle. This note mainly deals with this second problem for a family of systems with a homogeneous nonlinear part. While the condition that allows us to separate the existence and the nonexistence of limit cycles can be described, it is very intricate. {\textcopyright} 2004 American Mathematical Society.",

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N2 - For a given family of planar differential equations it is a very difficult problem to determine an upper bound for the number of its limit cycles. Even when this upper bound is one it is not always an easy problem to distinguish between the case of zero and one limit cycle. This note mainly deals with this second problem for a family of systems with a homogeneous nonlinear part. While the condition that allows us to separate the existence and the nonexistence of limit cycles can be described, it is very intricate. © 2004 American Mathematical Society.

AB - For a given family of planar differential equations it is a very difficult problem to determine an upper bound for the number of its limit cycles. Even when this upper bound is one it is not always an easy problem to distinguish between the case of zero and one limit cycle. This note mainly deals with this second problem for a family of systems with a homogeneous nonlinear part. While the condition that allows us to separate the existence and the nonexistence of limit cycles can be described, it is very intricate. © 2004 American Mathematical Society.

KW - Bifurcation

KW - Limit cycle

KW - Rigid system

KW - Rotated vector field

U2 - https://doi.org/10.1090/S0002-9939-04-07542-2

DO - https://doi.org/10.1090/S0002-9939-04-07542-2

M3 - Article

VL - 133

SP - 751

EP - 758

ER -