236
D. Lloyd
Fig. 14.3 Mass spectrometric determination of dissolved O 2 , CO 2 and H 2 S during complex oscillations in a yeast continuous fermentation experiment. Data are from Roussel and Lloyd [144],
courtesy of Dr. MR. Roussel
across multiple time scales of the multioscillator was determined by well-established
principles [6]. Thus both the dissolved O 2 and the CO 2 data gave a perfect correlation
between oscillators in the 13 h, 40 min, and 4 min domains. Relative Dispersional
Analysis (RDA) of double log plots gave an inverse power relationship with a fractal
dimension D f = (1.0) implying that RD is constant with scale (i.e., the time series
look statistically-similar on all time scales). Long-term memory from min to hours
is implicit in the oscillatory behaviour, and provides for coherence of the whole
system. Power spectral analysis (PSA) also indicated an inverse power law proportional to 1/f
ß , with a value of ß = 1.95, close to that of coloured noise, and again as
expected for a system that shows deterministic chaos. The basic principles underlying the fractal nature of a chaotic time series has previously been explained [84].
D. Lloyd
Fig. 14.3 Mass spectrometric determination of dissolved O 2 , CO 2 and H 2 S during complex oscillations in a yeast continuous fermentation experiment. Data are from Roussel and Lloyd [144],
courtesy of Dr. MR. Roussel
across multiple time scales of the multioscillator was determined by well-established
principles [6]. Thus both the dissolved O 2 and the CO 2 data gave a perfect correlation
between oscillators in the 13 h, 40 min, and 4 min domains. Relative Dispersional
Analysis (RDA) of double log plots gave an inverse power relationship with a fractal
dimension D f = (1.0) implying that RD is constant with scale (i.e., the time series
look statistically-similar on all time scales). Long-term memory from min to hours
is implicit in the oscillatory behaviour, and provides for coherence of the whole
system. Power spectral analysis (PSA) also indicated an inverse power law proportional to 1/f
ß , with a value of ß = 1.95, close to that of coloured noise, and again as
expected for a system that shows deterministic chaos. The basic principles underlying the fractal nature of a chaotic time series has previously been explained [84].