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arXiv · 2312.01452

On the number of limit cycles for piecewise polynomial holomorphic systems

Armengol Gasull·Gabriel Rondón·Paulo R. da Silva
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Abstract

In this paper we are concerned with determining lower bounds of the number of limit cycles for piecewise polynomial holomorphic systems with a straight line of discontinuity. We approach this problem with different points of view: study of the number of zeros of the first and second order averaging functions, or with the control of the limit cycles appearing from a monodromic equilibrium point via a degenerated Andronov-Hoph type bifurcation, adding at the very end the sliding effects. We also use the Poincaré-Miranda theorem for obtaining an explicit piecewise linear holomorphic systems with 3 limit cycles, result that improves the known examples in the literature that had a single limit cycle.

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Armengol Gasull, Gabriel Rondón, Paulo R. da Silva. 2023-12-03. On the number of limit cycles for piecewise polynomial holomorphic systems. https://arxiv.org/abs/2312.01452

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