Document Type


Date of Award

Spring 5-31-2002

Degree Name

Doctor of Philosophy in Mathematical Sciences - (Ph.D.)


Mathematical Sciences

First Advisor

Amitabha Koshal Bose

Second Advisor

Denis L. Blackmore

Third Advisor

Victoria Booth

Fourth Advisor

Gyorgy Buzsaki

Fifth Advisor

Farzan Nadim


The Sharp Wave-associated Ripple is a high-frequency, extracellular recording observed in the rat hippocampus during periods of immobility. During the ripple, pyramidal cells synchronize over a short period of time despite the fact that these cells have sparse recurrent connections. Additionally, the timing of synchronized pyramidal cell spiking may be critical for encoding information that is passed on to post-hippocampal targets. Both the synchronization and precision of pyramidal cells is believed to be coordinated by inhibition provided by a vast array of interneurons. This dissertation proposes a minimal model consisting of a single interneuron which synapses onto a network of uncoupled pyramidal cells. It is shown that fast decaying, high-frequency, depressing inhibition is capable of rapidly synchronizing the pyramidal cells and modulating spike timing. In addition, these mechanisms are robust in the presence of intracellular noise. The existence and stability of synchronous, periodic solutions using geometric singular perturbation techniques are proven. The effects of synaptic strength, synaptic recovery, and inhibition frequency are discussed. In contrast to prior work, which suggests that the ripple is produced by homogeneous populations of either pyramidal cells or interneurons, the results presented here suggest that cooperation between interneurons and pyramidal cells is necessary for ripple genesis.

Included in

Mathematics Commons



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