Transition from persistent to antipersistent correlation in biological systems

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Abstract
Fractal analyses on several noiselike time series from biological experiments reveal transitions from persistent correlation to antipersistent correlation. In this paper, we discuss several simple random walk models which produce such transitions, and therefore are candidates for the mechanisms that may be present in these biological systems. These mechanisms are a correlated fractal random walk that is constrained by a threshold or environmental or inertial forces. We find that persistent correlations for brief time intervals can arise by inertial movement, while for the long time intervals antipersistent correlations can arise from the fact that the natural system is bounded. We also estimate the transition point between these two correlation behaviors. The results agree with the experiment in magnitude.

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