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Crossing limit cycles of planar discontinuous piecewise differential systems formed by isochronous centres

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Author(s):
Buzzi, Claudio A. ; Carvalho, Yagor Romano ; Llibre, Jaume
Total Authors: 3
Document type: Journal article
Source: DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL; v. 37, n. 4, p. 19-pg., 2022-09-28.
Abstract

These last years an increasing interest appeared in studying the planar discontinuous piecewise differential systems motivated by the rich applications in modelling real phenomena. The understanding of the dynamics of these systems has many difficulties. One of them is the study of their limit cycles. In this paper, we study the maximum number of crossing limit cycles of some classes of planar discontinuous piecewise differential systems separated by a straight line and formed by combinations of linear centres (consequently isochronous) and cubic isochronous centres with homogeneous nonlinearities. For these classes of planar discontinuous piecewise differential systems we solved the extension of the 16th Hilbert problem, i.e. we provide an upper bound for their maximum number of crossing limit cycles. (AU)

FAPESP's process: 21/14695-7 - Limit cycles, regularization and period function of piecewise smooth planar systems.
Grantee:Yagor Romano Carvalho
Support Opportunities: Scholarships in Brazil - Post-Doctoral
FAPESP's process: 16/00242-2 - Bifurcation of piecewise smooth systems with singular borders via regularization
Grantee:Yagor Romano Carvalho
Support Opportunities: Scholarships in Brazil - Doctorate
FAPESP's process: 19/10269-3 - Ergodic and qualitative theories of dynamical systems II
Grantee:Claudio Aguinaldo Buzzi
Support Opportunities: Research Projects - Thematic Grants
FAPESP's process: 18/05098-2 - Study of limit cycles in piecewise smooth systems on the cylinder
Grantee:Yagor Romano Carvalho
Support Opportunities: Scholarships abroad - Research Internship - Doctorate