Dynamical Systems - History - Backgrounds |
Balthazar van der Pol (1889-1959)
Balthazar van der Pol was a Dutch electrical engineer who initiated
modern experimental dynamics in the laboratory during the 1920's and
1930's.
Van der Pol investigated electrical circuits employing vacuum tubes
and found that they have stable oscillations, now called limit cycles.
When these circuits are driven with a signal whose frequency is near that
of the limit cycle, the resulting periodic response shifts its frequency
to that of the driving signal. That is to say, the circuit becomes
"entrained" to the driving signal. The waveform, or signal shape, however,
can be quite complicated and contain a rich structure of harmonics and
subharmonics.
In the September 1927 issue of the British journal Nature, he and his colleague van der
Mark reported that an "irregular noise" was heard at certain driving
frequencies between the natural entrainment frequencies. By reconstructing
his electronic tube circuit, we now know that they had discovered deterministic
chaos. Their paper is probably one of the first experimental reports
of chaos---something that they failed to pursue in more detail.
Van der Pol built a number of electronic circuit models of the human
heart to study the range of stability of heart dynamics. His
investigations with adding an external driving signal were analogous to
the situation in which a real heart is driven by a pacemaker. He was
interested in finding out, using his entrainment work, how to stabilize a
heart's irregular beating or "arrhythmias". |
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