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Journal article
Existence and Stability of Standing Pulses in Neural Networks: I. Existence
SIAM journal on applied dynamical systems, v 4(2), pp 217-248
01 Jan 2005
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 nonsaturating 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.
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Details
- Title
- Existence and Stability of Standing Pulses in Neural Networks: I. Existence
- Creators
- Yixin GuoCarson C Chow
- Publication Details
- SIAM journal on applied dynamical systems, v 4(2), pp 217-248
- Publisher
- Society for Industrial and Applied Mathematics
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000230427900001
- Scopus ID
- 2-s2.0-20444449197
- Other Identifier
- 991020531965504721
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- Collaboration types
- Domestic collaboration
- Web of Science research areas
- Mathematics, Applied
- Physics, Mathematical