Nonlinear Dynamical Systems in
Comment on Guillot
I read this paper with great interest having particpated, with Henry Szechtman and David Eilam in their work on locomotor behavior in rats treated with chronic quinpirole. In that study, to appear in Behavioral Neuroscience, we used ergodic theoretic methods to study the temporal organization of locomotor behavior in rats, allowed to move freely within an open field, following chronic injections of quinpirole, a dopamine agonist. Not included in that study were some suggestive results which bear some similarity to those being reported here. We found weak evidence for two levels of control governing the spatiotemporal organization of such locomotor activity. At the lowest level, responsible for the selection of individual actions, we found evidence of simple stochasticity, or at the very least, very high dimensional chaos. Hurst exponents were near 0.5, suggesting that the sequencing was identical to a random walk on the action space. The higher level concerned the global organization of activity appearing as the block size was increased. Markov entropies decreased indicating an increase in order and the Hurst exponent increased, again showing a departure from simple Brownian motion. However both remained high so that although structure was emerging, it was at best due to high dimensional chaos though of lower dimensionality than for the lower system. It suggested to us that stochasticity was an inherent feature of the action selection system and that what was critical were the sources of correlation and order appearing from these higher level systems. In your paper you provide evidence for an even higher level order emerging from circadian pacemakers.
These sources of order appear in the temporal structure of the data. A intersting question concerns how they are effected at the neruonal or systemic level and whether they correspond to anatomical hierarchies, or whether these hierachies are purely functional.
Wed Dec 9