Oscillations in the field potential, that can be associated with behavior, have been identified experimentally in cortical structures of humans and several animal species. During fast field oscillations (gamma oscillations (40--80 Hz) and sharp waves (100--200 Hz)) cortical neurons typically discharge irregularly and at much lower frequency than that of the field potential. It is not clear what is the mechanism that leads to the synchronization and rhythmic firing of neuronal populations given the almost Poisson-like discharge statistics of single cells. One aim of this dissertation is to investigate the seeming dichotomy between the rhythmicity of the field potential and the irregular discharge of single cells using an approach based on the neuron's firing probability rather than on the knowledge of exact spike timing. We use neuronal networks composed of inhibitory and excitatory conductance-based model neurons to address the question of what determines the frequency of fast network oscillations. We show that the population dynamics can be predicted on the basis of the synaptic and single cell parameters. Furthermore, we investigate a second type of field oscillations, theta oscillations (4--8 Hz), that are thought to play an important role in cognitive processes. Neurons have been identified that show inherent rhythmic firing at theta frequency and are thought to play the role of pacemakers for neuronal populations. We show that pacemaker neurons can engage neuronal populations into rhythmic firing while being in reciprocal connections with them. We propose a network model for hippocampal theta oscillations and investigate the contributions of different classes of inhibitory and excitatory neurons to the field oscillations on the basis of their discharge characteristics that have been found experimentally in vivo. These network models allow us to demonstrate how different mechanism can lead to oscillations in distinct frequency bands and we provide a framework that helps us to understand the emergence and interaction of different cortical rhythms. This thesis presents an advance in the direction of network oscillations that incorporate realistic single cell features and network parameters.
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