Journal
PHYSICA D-NONLINEAR PHENOMENA
Volume 238, Issue 3, Pages 253-263Publisher
ELSEVIER
DOI: 10.1016/j.physd.2008.10.008
Keywords
Neuronal network; Synaptic depression; Periodic orbit; Dynamical systems
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Funding
- National Science Foundation [DMS-0817703, DMS-0615168]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [0817703] Funding Source: National Science Foundation
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We study a network of m identical excitatory cells projecting excitatory synaptic connections onto a single inhibitory interneuron, which is reciprocally coupled to all excitatory cells through inhibitory synapses possessing short-term synaptic depression. We find that such a network with global inhibition possesses multiple stable activity patterns with distinct periods, characterized by the clustering of the excitatory cells into synchronized sub-populations. We prove the existence and stability of n-cluster solutions in a m-cell network. Using methods of geometric singular perturbation theory, we show that any n-cluster solution must satisfy a set of consistency conditions that can be geometrically derived. We then characterize the basin of attraction of each solution. Although frequency dependent depression is not necessary for multistability, we discuss how it plays a key role in determining network behavior. We find a functional relationship between the level of synaptic depression, the number of clusters and the interspike interval between neurons. This relationship is much less pronounced in the absence of depression. implications for temporal coding and memory storage are discussed. (c) 2008 Elsevier B.V. All rights reserved.
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