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.
Show me the PDF file (380 KB), TEX file, and other files for this article.
 |
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 |
Return to the EJDE web page