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Limit cycles in 4-star-symmetric planar piecewise linear systems

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Abstract Our interest is centered in the study of the number of limit cycles for nonsmooth piecewise linear vector fields on the plane when the switching curve is x y… Click to show full abstract

Abstract Our interest is centered in the study of the number of limit cycles for nonsmooth piecewise linear vector fields on the plane when the switching curve is x y = 0 . We consider the symmetric case. That is, one vector field defined in the odd quadrants and the other in the even ones. We deal with equilibrium points of center-focus type, with matrices in real Jordan form, in each vector field when the infinity is monodromic. In this case, we provide the center classification at infinity, we prove that the maximum order of a weak focus is five. Moreover, we show the existence of systems exhibiting five limit cycles bifurcating from infinity.

Keywords: planar piecewise; limit cycles; cycles star; symmetric planar; star symmetric; piecewise linear

Journal Title: Journal of Differential Equations
Year Published: 2020

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