The number of limit cycles of certain polynomial differential equations

T. R. Blows

Research output: Contribution to journalArticlepeer-review

87 Scopus citations


Two-dimensional differential systems x=P(x, y), y= Q(x, y) are considered, where P and Q are polynomials. The question of interest is the maximum possible number of limit cycles of such systems in terms of the degree of P and Q. An algorithm is described for determining a so-called focal basis; this can be implemented on a computer. Estimates can then be obtained for the number of small-amplitude limit cycles. The technique is applied to certain cubic systems; a class of examples with exactly five small-amplitude limit cycles is constructed. Quadratic systems are also considered.

Original languageEnglish (US)
Pages (from-to)215-239
Number of pages25
JournalProceedings of the Royal Society of Edinburgh: Section A Mathematics
Issue number3-4
StatePublished - 1984

ASJC Scopus subject areas

  • General Mathematics


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