Equations relevant to behavior

Alex Proekt’s data fit a power law, a simple exponential equation denoting scale-free dynamics. See Assay Box.

On a circadian time scale, the activity of individual animals all fit this equation when the lights went out (the transition from lowest arousal to highest), demonstrating a remarkable lawfulness of arousal-dependent behavior. More surprising: there was reverse symmetry when the the lights went back on – – – the same equation, reversed, fit the individual behavioral data.

Overall, the fluctuations of CNS arousal in any vertebrate, including humans, are conceived as following a differential equation in which a significant amount of the data (about one-third) are accounted for by a “generalized CNS arousal” term Ag. See University of Cambridge book, p. 26

Claude Shannon’s equation expressing information theory – – the quantity of information without any reference to its exact content or meaning. Analogously, Generalized CNS Arousal accounts for the initiation of behavior without any reference to the specific motivation connected with the behavior. See University of Cambridge book p.119.

An equation which can generate chaotic dynamics. Physicist Jayanth Banavar and I (2007) were intrigued by the power of non-linear dynamics to generate marked amplifications of tiny perturbations, as a possible means of initiating behavioral trajectories quickly when necessary.

A Gaussian function which matched arousal behavior in a so-called “food anticipatory activity” assay (LeSauter et al. 2009). This equation’s close match to the data suggests a series of binary yes/no choices ( go/no go choices) with an increasing proportion of “go” decisions as feeding time draws near.