Electron. J. Diff. Equ., Vol. 2010(2010), No. 161, pp. 1-25.

Analysis of a quadratic system obtained from a scalar third order differential equation

Fabio Scalco Dias, Luis Fernando Mello

Abstract:
In this article, we study the nonlinear dynamics of a quadratic system in the three dimensional space which can be obtained from a scalar third order differential equation. More precisely, we study the stability and bifurcations which occur in a parameter dependent quadratic system in the three dimensional space. We present an analytical study of codimension one, two and three Hopf bifurcations, generic Bogdanov-Takens and fold-Hopf bifurcations.

Submitted February 15, 2010. Published November 10, 2010.
Math Subject Classifications: 70K50, 70K20, 34C60.
Key Words: Bifurcation; Hopf bifurcation; Bogdanov-Takens bifurcation; fold-Hopf bifurcation; limit cycle; stability; quadratic system.

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Fabio Scalco Dias
Instituto de Ciências Exatas, Universidade Federal de Itajubá
Avenida BPS 1303, Pinheirinho, CEP 37.500-903
Itajubá MG, Brazil
email: scalco@unifei.edu.br
Luis Fernando Mello
Instituto de Ciências Exatas, Universidade Federal de Itajubá
Avenida BPS 1303, Pinheirinho, CEP 37.500-903
Itajubá MG, Brazil
email: lfmelo@unifei.edu.br, Tel 00-55-35-36291217, Fax 00-55-35-36291140

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