DISTRIBUTIONS OF LOCAL MANDELBROT-HURST EXPONENTS: MOTOR ACTIVITY IN FETAL RATS OF COCAINIZED MOTHERS AND MANIC-DEPRESSIVE PATIENTS

Abstract

Intermittency, in which the normalized weight of large fluctuations grows for increasingly longer statistical samples, is seen as irregular bursting activity in time and is characteristic of the behavior of many brain and behavioral systems. This pattern has been related to the brain-stabilizing interplay of the general mechanisms of silence-evoked sensitization and activity-evoked desensitization, which can be found at most levels of neurobiological function and which vary more smoothly and at much longer times than the phasic observables. We use both the global Mandelbrot-Hurst exponent and the distribution of local Mandelbrot-Hurst exponents, in combination with dynamical entropies, to quantitate the property of nonuniform persistence which we treat as both deterministically expansive and statistically diffusive. For example, varying the parameter of the one-dimensional, Manneville-Pomeau intermittency map generated time series which demonstrated systematic changes in these statistical indices of persistence. Relatively small doses of cocaine administered to pregnant rats increased statistical indices of expansiveness and persistence in fetal motor behavior. These techniques also model and characterize a breakdown of statistical scaling in 72-hour time series of the amount of motor activity in some hospitalized manic-depressive patients.