I read a lengthy description (I think it was James P. Hogan's Reality Interrupt) and at that time I checked the numbers, which checked out; Hogan was way down alternative-science alley, but he usually did do his research.
His "brain emulator" was based on a cupboard-sized stack of silicon chips (probably achievable now) containing around 100 billion "neuristors", each composed of a tiny CPU and a memory of two kilobit - or was it kilobytes?. The chip was actually a latticework through which a dense cooling fluid was continuously circulated.
The power requirement was in the hundreds of kilowatts range, so the actual machinery, with heat pumps, fans etc., was way larger than a head - more like a large room.
Comparing these numbers with StephenG's answer, they aren't that far away, and Hogan's were probably based on the same assumptions.
Solving an ordinary differential equation of this kind, with dedicated hardware, seems way less costly than StephenG's estimates by almost three orders of magnitude.
Also, it stands to reason that a sequence of neural operations would not be completely unrelated, but instead (very probably) linked together, so that there would be ways of optimizing results and saving time.
A major difference lies in neuron firing frequency - while true that a neuron
has a maximum firing rate of one thousand per second, the average rate is way lower by almost four orders of magnitude.
So, the actual transition frequency and power requirements go well down, back into the range estimated by Hogan - around 100 Gflops without any optimizations.
It is somewhat disturbing that these numbers also happen to match the computing specification of Intel's "Movidius" deep neural processor...
(And just a few days ago, our power requirements got further reduced. We might be able to fit this in a head after all, and maybe power it from a human metabolism and a Seebeck converter).