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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.

- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E82-A No.9 pp.1883-1887

- Publication Date
- 1999/09/25

- Publicized

- Online ISSN

- DOI

- Type of Manuscript
- Special Section PAPER (Special Section on Nonlinear Theory and Its Applications)

- Category

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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 -