On the Number of Limit Cycles for Piecewise Polynomial Holomorphic Systems
Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Rondon Vielma, Gabriel Alexis (São Paulo State University. Institute of Biosciences, Humanities and Exact Sciences)
da Silva, Paulo Ricardo (São Paulo State University. Institute of Biosciences, Humanities and Exact Sciences)

Date:	2024
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. Initially, we study the number of zeros of the first- and second-order averaging functions. We also use the Lyapunov quantities to produce limit cycles appearing from a monodromic equilibrium point via a degenerated Andronov-Hopf type bifurcation, adding at the very end the sliding effects. Finally, we use the Poincaré-Miranda theorem for obtaining an explicit piecewise linear holomorphic system with 3 limit cycles, a result that improves the known examples in the literature that had a single limit cycle.
Grants:	Agencia Estatal de Investigación PID2019-104658GB-I00 Agencia Estatal de Investigación PID2022-136613NB-I00 Agencia Estatal de Investigación CEX2020-001084-M Agència de Gestió d'Ajuts Universitaris i de Recerca 2021/SGR-00113
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, la comunicació pública de l'obra i la creació d'obres derivades, fins i tot amb finalitats comercials, sempre i quan es reconegui l'autoria de l'obra original.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Piecewise polynomial holomorphic systems ; Limit cycles ; Averaging method ; Lyapunov quantities ; Poincaré-Miranda theorem
Published in:	SIAM Journal on Applied Dynamical Systems, Vol. 23, Issue 3 (September 2024) , p. 2593-2622, ISSN 1536-0040

DOI: 10.1137/23M1620922

Postprint 30 p, 564.6 KB

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