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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.)

Transcritical and zero-Hopf bifurcations in the Genesio system

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Author(s):
Cardin, Pedro Toniol ; Llibre, Jaume
Total Authors: 2
Document type: Journal article
Source: NONLINEAR DYNAMICS; v. 88, n. 1, p. 547-553, APR 2017.
Web of Science Citations: 3
Abstract

In this paper we study the existence of transcritical and zero-Hopf bifurcations of the third-order ordinary differential equation x (x) triple over dot + a<(x)double over dot> + b (b) over dot +cx - x(2) = 0, called the Genesio equation, which has a unique quadratic nonlinear term and three real parameters. More precisely, writing this differential equation as a first-order differential system in we prove: first that the system exhibits a transcritical bifurcation at the equilibrium point located at the origin of coordinates when and the parameters (a, b) are in the set [(a,b) is an element of R-2 : b not equal -]\textbackslash{}[(0,b)is an element of R-2: b > 0], and second that the system has a zero-Hopf bifurcation also at the equilibrium point located at the origin when and a = c = 0 and b > 0. (AU)

FAPESP's process: 13/24541-0 - Ergodic and qualitative theory of dynamical systems
Grantee:Claudio Aguinaldo Buzzi
Support Opportunities: Research Projects - Thematic Grants