II Maximum Multiplicity

From the discussion above, we need only look for multiple roots of eq. (39) to find the maximum value of n for our problem. For v = V2/2 and y = 12, w = 12 is a triple root of eq. (39), the most degenerate root obtained for any values of v and y. Therefore, we would expect that the value of n is 6 (star 

FIGURE 11 Nineteen qualitatively different bifurcation diagrams for wigwam singularity. 

FIGURE 12 Global bifurcation diagrams for eq. (18) near a wigwam singularity. 

An example will help to clear this point up. Fixing the value of y at 15, we can compute the cusp of fifth-order (or butterfly) singular points originating from the sixth-order singularity in the feasible region. When these points are plotted in the v-B plane, the result is the upper graph in Fig. 13. Choosing v and B to have the values 0.7520 and 930,000, the hysteresis variety projected 

FIGURE 13 Fifth-order singularities (top) and hysteresis variety (bottom) for y = 15, near wigwam singularity. 

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