Linear theory and type of bifurcation

This discrepancy is in line with other observed quantitative discrepancies such as in the threshold behaviour when a stochastic component is present in the applied voltage [96]. As already mentioned, the most drastic non-standard behaviour, which is not understood from the SM, is the observed Hopf bifurcation in sufficiently thin and clean specimens [18, 41-43, 49-51] and the very small hysteresis sometimes observed at threshold [38-40, 47], In fact a little further above threshold (but still near it) the amplitude of the pattern does appear to coincide reasonably with the results of the weakly non-linear theory [59], 

Since the measurements on RBC exhibit such beautiful quantitative agreement with theory one has concluded that the electrodynamic part of the basic equations needs improvement. This was the motivation for introducing the WEM (Section 13.2). The linear stability calculations for the conductive mode have been carried out within this model [48, 49] using the same approximations which led to the analytic threshold formulas within the SM [12-15]. It is found that there is an upward shift in the threshold, which may be quite small, and, more importantly, a Hopf bifurcation with critical frequency 

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