| In recent years theorists from physics, biology and the social sciences have suggested the possibility that a wide variety of complex systems might evolve to mathematically similar states. Two of the most commonly cited possibilities are a power law, a probability distribution that rises or declines at a steady exponential rate, and the edge of chaos, a region of transition between ordered and chaotic behavior. In related research, scientists have begun to investigate the tendency of trends in natural and human social systems to continue over time, regardless of the direction of the trend.;This dissertation examined records of state psychiatric hospital admissions and discharges for evidence of the presence of power laws, evolution to the edge of chaos, and trend persistence. Probability distributions were one-tailed, with evidence of power law behavior in the tails. Testing with the Lyapunov exponent, a standard test of the presence of deterministic chaos, indicated that daily admissions and discharges tended to approach the transition region between an orderly and a chaotic regime. Trend persistence was noted in all series of admissions and discharges. Stronger trend persistence was correlated with higher staff turnover. Trend persistence was also positively correlated with the geographic dispersion of admissions and discharges.;These findings carry implications for social work practice. The presence of a power law in a number of distributions of admissions and discharges implies the possibility that complex systems tend to evolve to this state independent of administrative control. and therefore that the power law may represent a limit on the possibilities of administrative control. Power law distributions tend to have long tails: thus, these distributions showed more unusually large events than would be expected under typical statistical assumptions. Trend persistence implies long runs of unusually high or low numbers of admissions and discharges, which might be expected to affect staff turnover and morale. |
