A class of differential systems of degree even with exact non-algebraic limit cycles

Abdelkrim Kina, Aziza Berbache, Ahmed Bendjeddou


Up until now all the polynomial differential systems for which
non-algebraic limit cycles are known explicitly have degree odd. Here we
show that already that there are polynomial systems of degree even has
an explicit limit cycle which is not algebraic. To our knowledge, there
are no such type of examples in the literature.


Planar polynomial differential system, first integral, non-algebraic limit cycle.

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DOI: http://dx.doi.org/10.24193/subbmath.2020.3.08


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