Differential and Integral Equations

Existence and attraction of a phase-locked oscillation in a delayed network of two neurons

Yuming Chen and Jianhong Wu

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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.

Article information

Differential Integral Equations, Volume 14, Number 10 (2001), 1181-1236.

First available in Project Euclid: 21 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 34K13: Periodic solutions
Secondary: 34K19: Invariant manifolds 34K20: Stability theory 34K60: Qualitative investigation and simulation of models 37N25: Dynamical systems in biology [See mainly 92-XX, but also 91-XX] 92C20: Neural biology


Chen, Yuming; Wu, Jianhong. Existence and attraction of a phase-locked oscillation in a delayed network of two neurons. Differential Integral Equations 14 (2001), no. 10, 1181--1236. https://projecteuclid.org/euclid.die/1356123098

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