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 language||English (US)|
|Number of pages||25|
|Journal||Proceedings of the Royal Society of Edinburgh Section A: Mathematics|
|State||Published - 1984|
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