Proceedings of the American Mathematical Society

Author(s): Yuming Chen; Ying Sue Huang; Jianhong Wu
Journal: Proc. Amer. Math. Soc. 128 (2000), 2365-2371.
MSC (2000): Primary 34K15, 92B20
Posted: February 25, 2000
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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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Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 34K15, 92B20

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: 10.1090/S0002-9939-00-05635-5
PII: S 0002-9939(00)05635-5
Keywords: Synchronization, slow oscillation, delay, neural network
Received by editor(s): September 19, 1998
Posted: 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 of article: Copyright 2000, American Mathematical Society

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