Histamine is a central neurotransmitter, it increases arousal via H1 receptors. This study examines the effect of ultra-diluted histamine on arousal through changes in the sleep pattern of Wistar rats. The spectral density in delta (0.5-2.5 Hz) band, one of the three major spectral components of the sleep-electroencephalogram, was analyzed against time. Rats were randomized to receive histamine 30c (histamine 30c, 0.05 ml every 20 min during the first 2 h orally), histamine intraperitoneal pre-treatment/histamine 30c (histamine 6mg/kg i.p., followed by histamine 30c) or solvent control. The mean delta band spectral density was lower in the histamine 30c and histamine pretreatment/histamine 30c groups than the control group. Significant differences between histamine 30c and baseline during the first 2 h imply an immediate effect. These results also suggest a dynamic process in which the system spontaneously evolves between two locally stationary states according to a power law. From the time perspective, the system approaches, asymptotically, an equifinal state.