Synchrony between mitral cells of the olfactory bulb has been found in several studies and may be important for downstream processing in higher brain areas. However, existing reports and computational models demonstrating synchrony induced through the mitral-granule circuit have measured mitral cells that are relatively proximal to each other. Since distal inhibitory inputs from the granule cells onto the lateral dendrites do not affect mitral cell spiking, it is not clear if or how distal glomeruli of mitral cells can synchronize with each other, especially when considering the sparseness of the mitral-granule circuit.

This thesis details experiments using small and larger mitral-granule computational networks that measure synchrony with respect to spatial separation of the glomeruli and describes factors that are necessary or promote distal interglomerular synchrony. It is shown that while a granule cell may not be proximal to both mitral cells that are widely separated, the paradox of not being able to provide a proximal correlated input to the mitral cells to drive synchrony is resolved when granule cells are themselves synchronized and therefore behave as a collective, correlated signal. Because the mitral-granule circuit is sparse, this dynamic is induced in larger populations of neurons and demonstrates that the network may use such sparsity to engage and disengage synchrony.

In addition to these conclusions, a novel method has been developed that models the membrane dynamics of neurons with a sum of exponential functions. This enables the computations to only be performed upon receiving synaptic events. The theory of this method is described and applied to the neural network of the olfactory bulb. When modeling the neurons and networks of the olfactory bulb, this method was 100-fold faster while exhibiting comparable dynamical behavior to networks comprised of neuron models that compute with ordinary differential equations. Therefore, this technique enables a more rapid exploration of neural networks to accelerate scientific discovery.