Desynchronization of large scale delayed neural networks
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- by Yuming Chen, Ying Sue Huang and Jianhong Wu PDF
- Proc. Amer. Math. Soc. 128 (2000), 2365-2371 Request permission
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.References
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Additional Information
- Yuming Chen
- Affiliation: Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada M3J 1P3
- MR Author ID: 363105
- 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
- MR Author ID: 226643
- Email: wujh@mathstat.yorku.ca
- 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
- © Copyright 2000 American Mathematical Society
- 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
- MathSciNet review: 1709744