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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.)

Periodic solutions and invariant torus in the Rossler system

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Author(s):
Candido, Murilo R. [1] ; Novaes, Douglas D. [1] ; Valls, Claudia [2]
Total Authors: 3
Affiliation:
[1] Univ Estadual Campinas, Dept Matemat, Rua Sergio Buarque de Holanda 651, BR-13083859 Campinas, SP - Brazil
[2] Univ Lisbon, Inst Super Tecn, Dept Matemat, Ave Rovisco Pais, P-1049001 Lisbon - Portugal
Total Affiliations: 2
Document type: Journal article
Source: Nonlinearity; v. 33, n. 9 SEP 2020.
Web of Science Citations: 0
Abstract

The Rossler system is characterized by a three-parameter family of quadratic 3D vector fields. There exist two one-parameter families of Rossler systems exhibiting a zero-Hopf equilibrium. For Rossler systems near to one of these families, we provide generic conditions ensuring the existence of a torus bifurcation. In this case, the torus surrounds a periodic solution that bifurcates from the zero-Hopf equilibrium. For Rossler systems near to the other family, we provide generic conditions for the existence of a periodic solution bifurcating from the zero-Hopf equilibrium. This improves currently known results regarding periodic solutions for such a family. In addition, the stability properties of the periodic solutions and invariant torus are analysed. (AU)

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: 19/10269-3 - Ergodic and qualitative theories of dynamical systems II
Grantee:Claudio Aguinaldo Buzzi
Support Opportunities: Research Projects - Thematic Grants
FAPESP's process: 18/07344-0 - 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: 18/16430-8 - Global dynamics of nonsmooth differential equations
Grantee:Douglas Duarte Novaes
Support Opportunities: Regular Research Grants