Coherent oscillations in modeled neuronal networks

Coherent oscillations, as they relate to neural systems, are of great interest to physicists, mathematicians, and biologists. I present the study of coherent oscillations in model neurons, specifically conductance based models and phase response curve (PRC) models, culminating in the application of periodic forcing of model networks in regard to disease states such as Parkinson's and epilepsy.;At the cellular level, ion channels in neuronal membranes are known to cause changes in neural network dynamics. The effect of mutated ion channels on the response of modeled neuronal oscillators is described, along with the study of how synaptic and intrinsic noise of individual model oscillators may be calculated from the PRC. These results are extended to networks of oscillators. Pulse-coupled oscillator theory is employed to predict changes in network dynamics, specifically the synchronizability of the network.;Another important factor affecting network dynamics is the topology, that is, the directional connectivity between individual neural oscillators. Simulations of a variety of networks reveal that two specific second-order connectivity statistics (two edge motifs), convergence and causal chains, determine the synchronizability of the network.;A Parkinsonian model of deep brain stimulation (DBS) is investigated consisting of periodic forcing of individual oscillators. This forcing may synchronize or desynchronize the network, depending on the frequency and amplitude of the periodic stimulation.;These concepts are all combined in the development of an epileptic seizure model, in which the coherence changes based on the firing rate of the population. The shift in synchrony during seizure states makes regulation through periodic forcing very challenging, as the entrainment of the network of cells is dependent on the frequency of cellular oscillation. A dynamic closed-loop feedback system is developed in order to control the synchrony of the modeled oscillator system, depending on the state of the epileptic seizure. This work is of interest to modelers of oscillators, networks, and disease states involving oscillating systems.