On The Phase Space Dynamics of Neuronal Systems: Model, Experiments, and Analysis.

We investigate the phase space dynamics of local systems of biological neurons in order to deduce the salient computational characteristics of such systems. We develop an abstract physical system that models local systems of spiking biological neurons. The system is based on a limited set of realistic assumptions and in consequence accommodates a wide range of neuronal models. An appropriate instantiation of the system is used to simulate the dynamics of a typical column in the neocortex. The results of the simulations demonstrate that the dynamical behavior of the system is akin to that observed in neurophysiological experiments. Analysis of local properties of flows in the phase space of the system reveals the classic characteristics of a chaotic system, namely, contraction, expansion, and folding. The criterion for the dynamics of the system to be sensitive to initial conditions is identified. Based on physiological parameters it is deduced that (a) periodic orbits in the region of the phase space corresponding to "normal operational conditions" are almost surely (with probability=1) unstable, (b) periodic orbits in the region of the phase space corresponding to "seizure like conditions" are almost surely stable, and (c) trajectories in the region of the phase space corresponding to "normal operational conditions" are almost surely sensitive to initial conditions. Based on these results preliminary conclusions are drawn about the computational nature of neocortical neuronal systems.Technical report DCS-TR-37