Small amplitude limit cycles of symmetric cubic systems

Terence R. Blows

doi:10.1016/j.camwa.2007.07.020

Small amplitude limit cycles of symmetric cubic systems

Terence R. Blows

Mathematics and Statistics

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

1 Scopus citations

Abstract

Hilbert's Sixteenth Problem concerns the number and relative position of limit cycles in a planar polynomial system of differential equations. We show, using multiple Hopf bifurcation from multiple fine foci, that limit cycle configurations of types (3, 3, -2, -2) and (2, 2, 1, 1, -1) occur in symmetric cubic systems.

Original language	English (US)
Pages (from-to)	2323-2328
Number of pages	6
Journal	Computers and Mathematics with Applications
Volume	56
Issue number	9
DOIs	https://doi.org/10.1016/j.camwa.2007.07.020
State	Published - Nov 2008

Keywords

Cubic systems
Hilbert's Sixteenth Problem
Hopf bifurcation
Limit cycles

ASJC Scopus subject areas

Modeling and Simulation
Computational Theory and Mathematics
Computational Mathematics

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10.1016/j.camwa.2007.07.020

Cite this

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title = "Small amplitude limit cycles of symmetric cubic systems",

abstract = "Hilbert's Sixteenth Problem concerns the number and relative position of limit cycles in a planar polynomial system of differential equations. We show, using multiple Hopf bifurcation from multiple fine foci, that limit cycle configurations of types (3, 3, -2, -2) and (2, 2, 1, 1, -1) occur in symmetric cubic systems.",

keywords = "Cubic systems, Hilbert's Sixteenth Problem, Hopf bifurcation, Limit cycles",

author = "Blows, \{Terence R.\}",

year = "2008",

month = nov,

doi = "10.1016/j.camwa.2007.07.020",

language = "English (US)",

volume = "56",

pages = "2323--2328",

journal = "Computers and Mathematics with Applications",

issn = "0898-1221",

publisher = "Elsevier Ltd",

number = "9",

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TY - JOUR

T1 - Small amplitude limit cycles of symmetric cubic systems

AU - Blows, Terence R.

PY - 2008/11

Y1 - 2008/11

N2 - Hilbert's Sixteenth Problem concerns the number and relative position of limit cycles in a planar polynomial system of differential equations. We show, using multiple Hopf bifurcation from multiple fine foci, that limit cycle configurations of types (3, 3, -2, -2) and (2, 2, 1, 1, -1) occur in symmetric cubic systems.

AB - Hilbert's Sixteenth Problem concerns the number and relative position of limit cycles in a planar polynomial system of differential equations. We show, using multiple Hopf bifurcation from multiple fine foci, that limit cycle configurations of types (3, 3, -2, -2) and (2, 2, 1, 1, -1) occur in symmetric cubic systems.

KW - Cubic systems

KW - Hilbert's Sixteenth Problem

KW - Hopf bifurcation

KW - Limit cycles

UR - https://www.scopus.com/pages/publications/52049087597

UR - https://www.scopus.com/inward/citedby.url?scp=52049087597&partnerID=8YFLogxK

U2 - 10.1016/j.camwa.2007.07.020

DO - 10.1016/j.camwa.2007.07.020

M3 - Article

AN - SCOPUS:52049087597

SN - 0898-1221

VL - 56

SP - 2323

EP - 2328

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

IS - 9

ER -

Small amplitude limit cycles of symmetric cubic systems

Abstract

Keywords

ASJC Scopus subject areas

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