THE PHASE-SPACE DYNAMICS OF SYSTEMS OF SPIKING NEURONS
Arunava Banerjee, Haym Hirsh · 2001
This thesis investigates the dynamics of systems of neurons in the brain. It considers two ques-tions: (1) Are there coherent spatiotemporal structures in the dynamics of neuronal systems that can denote discrete computational states, and (2) If such structures exist, what restrictions do the dynamics of the system at the physical level impose on the dynamics of the system at the corresponding abstracted computational level. These problems are addressed by way of an investigation of the phase-space dynamics of a general model of local systems of biological neurons. An abstract physical system is constructed based on a limited set of realistic assumptions about the biological neuron. The system, in consequence, accommodates a wide range of neu-ronal models. Appropriate instantiations of the system are used to simulate the dynamics of a typical column in the neocortex. The results demonstrate that the dynamical behavior of the system is akin to that observed in neurophysiological experiments. Formal analysis of local properties of flows reveals contraction, expansion, and folding in different sections of the phase-space. A stochastic process is formulated in order to determine