Stationary bifurcation to limit cycles and heteroclinic cycles

M. Field, James W Swift

Research output: Contribution to journalArticle

33 Citations (Scopus)

Abstract

The authors consider stationary bifurcations with Z4.Z 24 symmetry. For an open set of cubic coefficients in the normal form, we prove the existence of a limit cycle with frequency approximately mod lambda mod -1 as lambda to 0. It is shown that there are two types of structurally stable heteroclinic cycles in this example, one of which is of a new type. They find the stability of all of the zeros and heteroclinic cycles which branch from the origin at the bifurcation. Novel techniques are needed for the calculation of stability for the new type of heteroclinic cycle, and the proof of existence of the limit cycles.

Original languageEnglish (US)
Article number001
Pages (from-to)1001-1043
Number of pages43
JournalNonlinearity
Volume4
Issue number4
DOIs
StatePublished - 1991
Externally publishedYes

Fingerprint

Heteroclinic Cycle
Limit Cycle
Bifurcation
cycles
Bifurcation (mathematics)
Open set
Normal Form
Branch
Symmetry
Zero
Coefficient
symmetry
coefficients

ASJC Scopus subject areas

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

Cite this

Stationary bifurcation to limit cycles and heteroclinic cycles. / Field, M.; Swift, James W.

In: Nonlinearity, Vol. 4, No. 4, 001, 1991, p. 1001-1043.

Research output: Contribution to journalArticle

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