Numerical analysis of fold-pitchfork bifurcation with symmetry and its application in the pipe flow

Abstract

In this paper, we study the numerical analysis of fold-pitchfork bifurcation with Z2 symmetry. For this purpose, explicit formulas for the critical coefficients of this bifurcation are obtained and non-degeneracy conditions of this bifurcation are determined. Then, local bifurcations, bifurcation curves and phase portraits are computed by MatCont toolbox. We will emphasize an example serving as a model of pipe flow

Keywords

• Bifurcation
• Map
• Critical Coefficients
• Symmetry
• Pipe flow.