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 6 mg/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.