Some cubic systems with several limit cycles

N. G. Lloyd; T. R. Blows; M. C. Kalenge

doi:10.1088/0951-7715/1/4/008

Some cubic systems with several limit cycles

N. G. Lloyd, T. R. Blows, M. C. Kalenge

Mathematics and Statistics

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Abstract

Two-dimensional systems x=P(x, y), y=Q(x,y) in which P and Q are cubic polynomials, are considered, and a number of classes with several limit cycles are described. Examples of systems with six small-amplitude limit cycles are given. Other classes of systems with several limit cycles are obtained by considering simultaneous bifurcation from a finite critical point and infinity. Simultaneous bifurcation from several critical points is investigated.

Original language	English (US)
Article number	008
Pages (from-to)	653-669
Number of pages	17
Journal	Nonlinearity
Volume	1
Issue number	4
DOIs	https://doi.org/10.1088/0951-7715/1/4/008
State	Published - 1988

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
General Physics and Astronomy
Applied Mathematics

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abstract = "Two-dimensional systems x=P(x, y), y=Q(x,y) in which P and Q are cubic polynomials, are considered, and a number of classes with several limit cycles are described. Examples of systems with six small-amplitude limit cycles are given. Other classes of systems with several limit cycles are obtained by considering simultaneous bifurcation from a finite critical point and infinity. Simultaneous bifurcation from several critical points is investigated.",

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N2 - Two-dimensional systems x=P(x, y), y=Q(x,y) in which P and Q are cubic polynomials, are considered, and a number of classes with several limit cycles are described. Examples of systems with six small-amplitude limit cycles are given. Other classes of systems with several limit cycles are obtained by considering simultaneous bifurcation from a finite critical point and infinity. Simultaneous bifurcation from several critical points is investigated.

AB - Two-dimensional systems x=P(x, y), y=Q(x,y) in which P and Q are cubic polynomials, are considered, and a number of classes with several limit cycles are described. Examples of systems with six small-amplitude limit cycles are given. Other classes of systems with several limit cycles are obtained by considering simultaneous bifurcation from a finite critical point and infinity. Simultaneous bifurcation from several critical points is investigated.

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Some cubic systems with several limit cycles

Abstract

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