Abstract
We present the analysis of a phase-shift sequence obtained from random transitions between periodic solutions of a biochemical dynamical model, formed by a system of three differential equations and which represent an instability-generating multienzymatic mechanism. The phase-shift series was studied in terms of Hurst’s rescaled range analysis. We found that the data were characterized by a Hurst exponent H = 0.69, which was clearly indicative of long-term trends. This result had a high significance level, as was confirmed through Monte Carlo simulations in which the data were scrambled in the series, destroying its original ordering. For these series we obtained a Hurst exponent which was consistent with the expectation of H = 0.5 for a random independent process. This clearly showed that, although the transitions between the periodic solutions were provoked randomly, the stochastic process obtained exhibited long-term persistence. The fractal dimension was also estimated and found to be consistent with the value of the Hurst exponent.
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Martinez de la Fuente, I., Martinez, L., Benitez, N. et al. Persistent behavior in a phase-shift sequence of periodical biochemical oscillations. Bull. Math. Biol. 60, 689–702 (1998). https://doi.org/10.1006/bulm.1997.0036
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DOI: https://doi.org/10.1006/bulm.1997.0036