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arXiv · 2204.00085

Bifurcation of limit cycles in piecewise quadratic differential systems with an invariant straight line

Leonardo P. C. da Cruz·Joan Torregrosa
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Abstract

We solve the center-focus problem in a class of piecewise quadratic polynomial differential systems with an invariant straight line. The separation curve is also a straight line which is not invariant. We provide families having at the origin a weak-foci of maximal order. In the continuous class, the cyclicity problem is also solved, being $3$ such maximal number. Moreover, for the discontinuous class but without sliding segment, we prove the existence of $7$ limit cycles of small amplitude.

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Leonardo P. C. da Cruz, Joan Torregrosa. 2022-03-31. Bifurcation of limit cycles in piecewise quadratic differential systems with an invariant straight line. https://arxiv.org/abs/2204.00085

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