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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

On the torus bifurcation in averaging theory

Full text
Author(s):
Candido, Murilo R. [1] ; Novaes, Douglas D. [1]
Total Authors: 2
Affiliation:
[1] Univ Estadual Campinas, Dept Matemat, Rua Sergio Banque de Holanda 651, Cidade Univ, BR-13083859 Campinas, SP - Brazil
Total Affiliations: 1
Document type: Journal article
Source: Journal of Differential Equations; v. 268, n. 8, p. 4555-4576, APR 5 2020.
Web of Science Citations: 0
Abstract

In this paper, we take advantage of the averaging theory to investigate a torus bifurcation in two-parameter families of 2D nonautonomous differential equations. Our strategy consists in looking for generic conditions on the averaged functions that ensure the existence of a curve in the parameter space characterized by a Neimark-Sacker bifurcation in the corresponding Poincare map. A Neimark-Sacker bifurcation for planar maps consists in the birth of an invariant closed curve from a fixed point, as the fixed point changes stability. In addition, we apply our results to study a torus bifurcation in a family of 3D vector fields. (C) 2019 Elsevier Inc. All rights reserved. (AU)

FAPESP's process: 18/07344-0 - Invariant Sets in differential Dynamical Systems: Periodic orbits, Invariant Tori and Algebraic surfaces.
Grantee:Murilo Rodolfo Cândido
Support Opportunities: Scholarships in Brazil - Post-Doctoral
FAPESP's process: 19/05657-4 - Bifurcations of nested invariant tori and invariant sets of Lotka-Volterra differential systems
Grantee:Murilo Rodolfo Cândido
Support Opportunities: Scholarships abroad - Research Internship - Post-doctor
FAPESP's process: 18/16430-8 - Global dynamics of nonsmooth differential equations
Grantee:Douglas Duarte Novaes
Support Opportunities: Regular Research Grants
FAPESP's process: 18/13481-0 - Geometry of control, dynamical and stochastic systems
Grantee:Marco Antônio Teixeira
Support Opportunities: Research Projects - Thematic Grants
FAPESP's process: 19/10269-3 - Ergodic and qualitative theories of dynamical systems II
Grantee:Claudio Aguinaldo Buzzi
Support Opportunities: Research Projects - Thematic Grants