2001 Existence and attraction of a phase-locked oscillation in a delayed network of two neurons
Yuming Chen, Jianhong Wu
Differential Integral Equations 14(10): 1181-1236 (2001). DOI: 10.57262/die/1356123098

Abstract

In this article, we study the network of two neurons with delay. Using the discrete Lyapunov functional of Mallet-Paret and Sell and the techniques developed recently by Krisztin, Walther and Wu (for the scalar case), we obtain a two-dimensional closed disk bordered by a phase-locked periodic orbit and we have a complete description about the structure of various heteroclinic connections in the global forward extension of a three-dimensional $C^1$-submanifold contained in the unstable set of the trivial solution.

Citation

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Yuming Chen. Jianhong Wu. "Existence and attraction of a phase-locked oscillation in a delayed network of two neurons." Differential Integral Equations 14 (10) 1181 - 1236, 2001. https://doi.org/10.57262/die/1356123098

Information

Published: 2001
First available in Project Euclid: 21 December 2012

zbMATH: 1023.34065
MathSciNet: MR1852459
Digital Object Identifier: 10.57262/die/1356123098

Subjects:
Primary: 34K13
Secondary: 34K19 , 34K20 , 34K60 , 37N25 , 92C20

Rights: Copyright © 2001 Khayyam Publishing, Inc.

Vol.14 • No. 10 • 2001
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