Some cubic systems with several limit cycles

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

Research output: Contribution to journalArticle

29 Citations (Scopus)

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 languageEnglish (US)
Article number008
Pages (from-to)653-669
Number of pages17
JournalNonlinearity
Volume1
Issue number4
DOIs
StatePublished - 1988
Externally publishedYes

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Limit Cycle
Polynomials
cycles
Critical point
critical point
Bifurcation
Two-dimensional Systems
infinity
polynomials
Infinity
Polynomial
Class

ASJC Scopus subject areas

  • Mathematical Physics
  • Statistical and Nonlinear Physics
  • Applied Mathematics
  • Mathematics(all)

Cite this

Some cubic systems with several limit cycles. / Lloyd, N. G.; Blows, Terence R; Kalenge, M. C.

In: Nonlinearity, Vol. 1, No. 4, 008, 1988, p. 653-669.

Research output: Contribution to journalArticle

Lloyd, N. G. ; Blows, Terence R ; Kalenge, M. C. / Some cubic systems with several limit cycles. In: Nonlinearity. 1988 ; Vol. 1, No. 4. pp. 653-669.
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