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Lower Bounds for local cyclicity for Kolmogorov Systems on planar piecewise vector fields.

Grant number: 22/03801-3
Support type:Scholarships abroad - Research Internship - Post-doctor
Effective date (Start): October 01, 2022
Effective date (End): September 30, 2023
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal researcher:Paulo Ricardo da Silva
Grantee:Luiz Fernando da Silva Gouveia
Supervisor abroad: Oleg Makarenkov
Home Institution: Instituto de Biociências, Letras e Ciências Exatas (IBILCE). Universidade Estadual Paulista (UNESP). Campus de São José do Rio Preto. São José do Rio Preto , SP, Brazil
Research place: University of Texas at Dallas (UT Dallas), United States  
Associated to the scholarship:20/04717-0 - Dynamical systems with symmetries and implicit differential equations, BP.PD

Abstract

Our main goal in this project is to perturbation Kolmogorov Systems on planar piecewise vector fields defined in two zones separated by a straight line and study how many limit cycles can be obtained.In addition, we intend to approach the Kolmogorov Systems through Sotomayor-Teixeira regularization. It is well known that different regularizations can lead to different ways of defining sliding solutions on. In addition, from a theoretical point of view, assuming only linear regularization would neglect a vast expanse of phenomena occurring in smooth systems approaching pointwisely to non-smooth ones. Therefore, our main goal at this point is to consider two Kolmogorov Systems and study the regularization when both $\varphi$ is a monotonic function and $\varphi$ is not a monotonic function.

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