dorsal/arxiv
View SchemaExistence and Stability of Standing Pulses in Neural Networks : I Existence
| Authors | Yixin Guo, Carson C. Chow |
|---|---|
| Categories | |
| ArXiv ID | q-bio/0407013 |
| URL | https://arxiv.org/abs/q-bio/0407013 |
| DOI | 10.1137/040609483 |
Abstract
We consider the existence of standing pulse solutions of a neural network integro-differential equation. These pulses are bistable with the zero state and may be an analogue for short term memory in the brain. The network consists of a single-layer of neurons synaptically connected by lateral inhibition. Our work extends the classic Amari result by considering a non-saturating gain function. We consider a specific connectivity function where the existence conditions for single-pulses can be reduced to the solution of an algebraic system. In addition to the two localized pulse solutions found by Amari, we find that three or more pulses can coexist. We also show the existence of nonconvex ``dimpled'' pulses and double pulses. We map out the pulse shapes and maximum firing rates for different connection weights and gain functions.
{
"annotation_id": "fec46d6c-ccc7-4b01-b4f8-5d131aac6b20",
"date_created": "2026-03-02T18:01:31.862000Z",
"date_modified": "2026-03-02T18:01:31.862000Z",
"file_hash": "b4b32b188c4b9640c93368f5f9960643d3cf85a7e9e18928201f69f41cb2fbb0",
"private": false,
"record": {
"abstract": "We consider the existence of standing pulse solutions of a neural network\nintegro-differential equation. These pulses are bistable with the zero state\nand may be an analogue for short term memory in the brain. The network consists\nof a single-layer of neurons synaptically connected by lateral inhibition. Our\nwork extends the classic Amari result by considering a non-saturating gain\nfunction. We consider a specific connectivity function where the existence\nconditions for single-pulses can be reduced to the solution of an algebraic\nsystem. In addition to the two localized pulse solutions found by Amari, we\nfind that three or more pulses can coexist. We also show the existence of\nnonconvex ``dimpled\u0027\u0027 pulses and double pulses. We map out the pulse shapes and\nmaximum firing rates for different connection weights and gain functions.",
"arxiv_id": "q-bio/0407013",
"authors": [
"Yixin Guo",
"Carson C. Chow"
],
"categories": [
"q-bio.NC",
"q-bio.QM"
],
"doi": "10.1137/040609483",
"title": "Existence and Stability of Standing Pulses in Neural Networks : I Existence",
"url": "https://arxiv.org/abs/q-bio/0407013"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "cf297ba5-2983-4286-983c-9cb546d895ec",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}