Differential and Integral Equations
- Differential Integral Equations
- Volume 14, Number 10 (2001), 1181-1236.
Existence and attraction of a phase-locked oscillation in a delayed network of two neurons
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.
Differential Integral Equations, Volume 14, Number 10 (2001), 1181-1236.
First available in Project Euclid: 21 December 2012
Permanent link to this document
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