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arXiv · 1709.00903

Uniqueness of Limit Cycles for Quadratic Vector Fields

José Luis Bravo·Manuel Fernández·Ignacio Ojeda·Fernando Sánchez
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Abstract

This article deals with the study of the number of limit cycles surrounding a critical point of a quadratic planar vector field, which, in normal form, can be written as $x'= a_1 x-y-a_3x^2+(2 a_2+a_5)xy + a_6 y^2$, $y'= x+a_1 y + a_2x^2+(2 a_3+a_4)xy -a_2y^2$. In particular, we study the semi-varieties defined in terms of the parameters $a_1,a_2,\ldots,a_6$ where some classical criteria for the associated Abel equation apply. The proofs will combine classical ideas with tools from computational algebraic geometry.

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José Luis Bravo, Manuel Fernández, Ignacio Ojeda, Fernando Sánchez. 2017-09-04. Uniqueness of Limit Cycles for Quadratic Vector Fields. https://arxiv.org/abs/1709.00903

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