Electronic Journal of Differential Equations,
Vol. 2010(2010), No. 161, pp. 1-25.

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

Authors: Fabio Scalco Dias   (Univ. Federal de Itajuba, Brazil)
         Luis Fernando Mello (Univ. Federal de Itajuba, Brazil)

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.