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Desynchronization of large scale delayed neural networks


Authors: Yuming Chen, Ying Sue Huang and Jianhong Wu
Journal: Proc. Amer. Math. Soc. 128 (2000), 2365-2371
MSC (2000): Primary 34K15, 92B20
DOI: https://doi.org/10.1090/S0002-9939-00-05635-5
Published electronically: February 25, 2000
MathSciNet review: 1709744
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Abstract:

We consider a ring of identical neurons with delayed nearest neighborhood inhibitory interaction. Under general conditions, such a network has a slowly oscillatory synchronous periodic solution which is completely characterized by a scalar delay differential equation with negative feedback. Despite the fact that the slowly oscillatory periodic solution of the scalar equation is stable, we show that the associated synchronous solution is unstable if the size of the network is large.


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Additional Information

Yuming Chen
Affiliation: Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada M3J 1P3
Email: yumingc@mathstat.yorku.ca

Ying Sue Huang
Affiliation: Department of Mathematics, Pace University, Pleasantville, New York 10570
Email: huang@risc.dac.pace.edu

Jianhong Wu
Affiliation: Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada M3J 1P3
Email: wujh@mathstat.yorku.ca

DOI: https://doi.org/10.1090/S0002-9939-00-05635-5
Keywords: Synchronization, slow oscillation, delay, neural network
Received by editor(s): September 19, 1998
Published electronically: February 25, 2000
Additional Notes: This research was partially supported by the Natural Sciences and Engineering Research Council of Canada.
Communicated by: Hal L. Smith
Article copyright: © Copyright 2000 American Mathematical Society

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