Piecewise linear differential systems with an algebraic line of separation
Armengol Gasull, Joan Torregrosa, Xiang Zhang
Abstract
We study the number of limit cycles of planar piecewise linear differential systems separated by a branch of an algebraic curve. We show that for each \(n\in\mathbb{N}\) there exist piecewise linear differential systems separated by an algebraic curve of degree \(n\) having [n/2] hyperbolic limit cycles. Moreover, when n=2,3, we study in more detail the problem, considering a perturbation of a center and constructing examples with 4 and 5 limit cycles, respectively. These results follow by proving that the set of functions generating the first order averaged function associated to the problem is an extended complete Chebyshev system in a suitable interval. For more information see https://ejde.math.txstate.edu/Volumes/2020/19/abstr.html