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Journal of Vcibration Testing and System Dynamics 2(3) (2018) 249--256 | DOI:10.5890/JVTSD.2018.09.005

Vinícius B. Silva$^{1}$; João P. Vieira$^{2}$; Edson D. Leonel$^{1}$,$^{3}$

$^{1}$ Departamento de Física, UNESP - Universidade Estadual Paulista, Av. 24A, 1515 - Bela Vista, 13506-900, Rio Claro, SP, Brazil

$^{2}$ Departamento de Matemática, UNESP - Universidade Estadual Paulista, Av. 24A, 1515 - Bela Vista, 13506-900, Rio Claro, SP, Brazil

$^{3}$ Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy

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Abstract

In this paper we prove the following theorem: consider a N-dimensional dynamical system that is reduced to its center manifold. If it is proved the system satisfies the conditions of a Hopf bifurcation theorem then the original system of differential equations escribing the dynamics can be rewritten in a simpler analytical expression that preserves the phase space topology. The theorem proposed and proven effectively reduces the work done to obtain the normal form for the class of dynamical systems with the ccurrence of Hopf bifurcation.

Acknowledgments

V.B.S. acknowledges FAPESP (2015/23142-0) for nancial support. EDL acknowledges support from CNPq (303707/2015-1) and FAPESP (2012/23688-5). The authors acknowledge fruitful discussions with Professor João Paulo Cerri.

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