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

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.

Keywords

• Bifurcation
• Hopf bifurcation
• Bogdanov-Takens bifurcation
• fold-Hopf bifurcation
• limit cycle
• stability
• quadratic system