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


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