Investigations of bifurcations of limit cycles in Z2-equivariant planar vector fields of degree 5

Jibin Li; H. S Y Chan; K. W. Chung

doi:10.1142/S0218127402005698

Investigations of bifurcations of limit cycles in Z₂-equivariant planar vector fields of degree 5

Jibin Li, H. S Y Chan, K. W. Chung

Department of Mathematics

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

39 Citations (Scopus)

Abstract

Some distributions of limit cycles of Z₂-equivariant planar perturbed Hamiltonian polynomial vector fields of degree 5 are investigated. These include examples of specific Z₂-equivariant fields and Z₄-equivariant fields having up to 23 limit cycles. The configurations of compound eyes are also obtained by using the bifurcation theory of planar dynamical systems and the method of detection functions.

Original language	English
Pages (from-to)	2137-2157
Journal	International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume	12
Issue number	10
DOIs	https://doi.org/10.1142/S0218127402005698
Publication status	Published - Oct 2002

Research Keywords

Hilbert's 16th problem
Limit cycles
Perturbed planar Hamiltonian systems
Second bifurcation

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title = "Investigations of bifurcations of limit cycles in Z2-equivariant planar vector fields of degree 5",

abstract = "Some distributions of limit cycles of Z2-equivariant planar perturbed Hamiltonian polynomial vector fields of degree 5 are investigated. These include examples of specific Z2-equivariant fields and Z4-equivariant fields having up to 23 limit cycles. The configurations of compound eyes are also obtained by using the bifurcation theory of planar dynamical systems and the method of detection functions.",

keywords = "Hilbert's 16th problem, Limit cycles, Perturbed planar Hamiltonian systems, Second bifurcation",

author = "Jibin Li and Chan, {H. S Y} and Chung, {K. W.}",

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Investigations of bifurcations of limit cycles in Z₂-equivariant planar vector fields of degree 5. / Li, Jibin; Chan, H. S Y; Chung, K. W.
In: International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, Vol. 12, No. 10, 10.2002, p. 2137-2157.

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

TY - JOUR

T1 - Investigations of bifurcations of limit cycles in Z2-equivariant planar vector fields of degree 5

AU - Li, Jibin

AU - Chan, H. S Y

AU - Chung, K. W.

PY - 2002/10

Y1 - 2002/10

N2 - Some distributions of limit cycles of Z2-equivariant planar perturbed Hamiltonian polynomial vector fields of degree 5 are investigated. These include examples of specific Z2-equivariant fields and Z4-equivariant fields having up to 23 limit cycles. The configurations of compound eyes are also obtained by using the bifurcation theory of planar dynamical systems and the method of detection functions.

AB - Some distributions of limit cycles of Z2-equivariant planar perturbed Hamiltonian polynomial vector fields of degree 5 are investigated. These include examples of specific Z2-equivariant fields and Z4-equivariant fields having up to 23 limit cycles. The configurations of compound eyes are also obtained by using the bifurcation theory of planar dynamical systems and the method of detection functions.

KW - Hilbert's 16th problem

KW - Limit cycles

KW - Perturbed planar Hamiltonian systems

KW - Second bifurcation

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U2 - 10.1142/S0218127402005698

DO - 10.1142/S0218127402005698

M3 - RGC 21 - Publication in refereed journal

SN - 0218-1274

VL - 12

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EP - 2157

JO - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

JF - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

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