On the Existence and Stability of Solutions in Self-Organizing Cortical Maps
Summary :
We analyze the dynamics of self-organizing cortical maps under the influence of external stimuli. We show that if the map is a contraction, then the system has a unique equilibrium which is globally asymptotically stable; consequently the system acts as a stable encoder of external input stimuli. The system converges to a fixed point representing the steady-state of the neural activity which has as an upper bound the superposition of the spatial integrals of the weight function between neighboring neurons and the stimulus autocorrelation function. The proposed theory also includes nontrivial interesting solutions.
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- IEICE TRANSACTIONS on Fundamentals Vol.E82-A No.9 pp.1883-1887
- Publication Date
- 1999/09/25
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- Special Section PAPER (Special Section on Nonlinear Theory and Its Applications)
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Anke MEYER-BASE, "On the Existence and Stability of Solutions in Self-Organizing Cortical Maps" in IEICE TRANSACTIONS on Fundamentals,
vol. E82-A, no. 9, pp. 1883-1887, September 1999, doi: .
Abstract: We analyze the dynamics of self-organizing cortical maps under the influence of external stimuli. We show that if the map is a contraction, then the system has a unique equilibrium which is globally asymptotically stable; consequently the system acts as a stable encoder of external input stimuli. The system converges to a fixed point representing the steady-state of the neural activity which has as an upper bound the superposition of the spatial integrals of the weight function between neighboring neurons and the stimulus autocorrelation function. The proposed theory also includes nontrivial interesting solutions.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e82-a_9_1883/_p
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@ARTICLE{e82-a_9_1883,
author={Anke MEYER-BASE, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={On the Existence and Stability of Solutions in Self-Organizing Cortical Maps},
year={1999},
volume={E82-A},
number={9},
pages={1883-1887},
abstract={We analyze the dynamics of self-organizing cortical maps under the influence of external stimuli. We show that if the map is a contraction, then the system has a unique equilibrium which is globally asymptotically stable; consequently the system acts as a stable encoder of external input stimuli. The system converges to a fixed point representing the steady-state of the neural activity which has as an upper bound the superposition of the spatial integrals of the weight function between neighboring neurons and the stimulus autocorrelation function. The proposed theory also includes nontrivial interesting solutions.},
keywords={},
doi={},
ISSN={},
month={September},}
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TY - JOUR
TI - On the Existence and Stability of Solutions in Self-Organizing Cortical Maps
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1883
EP - 1887
AU - Anke MEYER-BASE
PY - 1999
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E82-A
IS - 9
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - September 1999
AB - We analyze the dynamics of self-organizing cortical maps under the influence of external stimuli. We show that if the map is a contraction, then the system has a unique equilibrium which is globally asymptotically stable; consequently the system acts as a stable encoder of external input stimuli. The system converges to a fixed point representing the steady-state of the neural activity which has as an upper bound the superposition of the spatial integrals of the weight function between neighboring neurons and the stimulus autocorrelation function. The proposed theory also includes nontrivial interesting solutions.
ER -
English
