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

2022/03/31 by da Cruz, Leonardo P. C., Torregrosa, Joan · 1 citation
#34C07 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2204.00085

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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• Limit Cycles in Piecewise Quadratic Kolmogorov Systems

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