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Small-Amplitude Limit Cycles of Certain Planar Differential Systems

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Abstract

In this work we consider the polynomial differential system \(\dot{x} = -y + x f(y)\), \(\dot{y} =x + y f(x)\), where f is a polynomial. This system is a certain generalization of the classical Liénard system. For that system, we solve the center problem for such family and compute the order of degeneracy of a weak focus for obtaining the maximum number of small-amplitude limit cycles.

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Acknowledgements

The authors are grateful to the referee for his/her valuable comments and suggestions to improve this paper. The first author is partially supported by a MINECO/ FEDER Grant Number MTM2017-84383-P and an AGAUR (Generalitat de Catalunya) Grant Number 2017SGR 1276. The second author is supported by FCT/Portugal through UID/MAT/04459/2013.

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Correspondence to Jaume Giné.

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Giné, J., Valls, C. Small-Amplitude Limit Cycles of Certain Planar Differential Systems. Qual. Theory Dyn. Syst. 19, 53 (2020). https://doi.org/10.1007/s12346-020-00389-y

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