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

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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