Assume that at a bifurcation point (xc, Rc) = (0, 0), in addition to the usual criteria
Chapter 14, Problem 14.8.4(choose chapter or problem)
Assume that at a bifurcation point (xc, Rc) = (0, 0), in addition to the usual criteria for a bifurcation point, fR = 0 and fxx = 0. Using a Taylor series analysis, show that as an approximation, dx dt = fxRRx + fRRR 6 R3 + .... Assume fxR > 0. Show there are two cases depending on the sign of fRRR. Analyze stability using one-dimensional phase diagrams (assuming fxx > 0). Explain why this bifurcation is called pitchfork bifurcation.
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