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Summer Program Seminars 2006

Thursday, June 29, 2006 @ 10:00AM
Cullimore Hall, Room 611
New Jersey Institute of Technology

Analysis of Clustered Solutions in a Globally Inhibitory Network of Spiking Cells

Lakshmi Chandrasekaran

Department of Mathematical Sciences

New Jersey Institute of Technology

Newark, New Jersey

ABSTRACT

A neuronal network of cells may exhibit numerous patterns of activity some of which are quite complex and occur extensively in the nervous system.  These rhythmic activity patterns have a major role to play in processing sensory information.  We consider a globally inhibitory network that contains an inhibitory neuron which synapses onto multiple uncoupled excitatory neurons.  The inhibitory synapse is depressing.  Synaptic depression is the decrease in amplitude of the synaptic conductance in response to the firing of an action potential by the presynaptic neuron.  Each excitatory neuron is reciprocally coupled to the inhibitory neuron.  Here we prove the existence and stability of a 2-clustered solution and generalize it to n-clustered solutions.  Our analysis shows how synaptic depression determines the interspike interval for these different types of solutions.