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The number of limit cycles of certain polynomial differential equations

Published online by Cambridge University Press:  14 November 2011

T. R. Blows  and
N. G. Lloyd
T. R. Blows
Affiliation:
Department of Pure Mathematics, The University College of Wales, Aberystwyth, Dyfed
N. G. Lloyd
Affiliation:
Department of Pure Mathematics, The University College of Wales, Aberystwyth, Dyfed
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Synopsis

Two-dimensional differential systems

are considered, where P and Q are polynomials. The question of interest is the maximum possible numberof 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.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 98 , Issue 3-4 , 1984 , pp. 215 - 239
Copyright
Copyright © Royal Society of Edinburgh 1984

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