The MathNet Korea
Information Center for Mathematical Science

논문검색

Information Center for Mathematical Science

논문검색

Journal of Differential Equations
( Vol. 168 NO.1 / (2000))
On a Planar System Modelling a Neuron Network with Memory
Teresa Faria,
Pages. 129-149
Abstract We consider a delay differential equation modeling a network of two neurons
with memory. The situations without self-connections and two delays, and with self-
connections and two equal delays, are addressed in terms of local stability and
bifurcation analysis. In the first case, the dynamical behavior is studied by taking
one of the delays as the bifurcating parameter. Namely, the Hopf bifurcation, whose
existence was proven in former works, occurs as the delay crosses some critical
values and is completely described. Conditions ensuring the stability of the periodic
cycles are given. When self-connections are present, Hopf and pitchfork bifurcations
co-exist and the equation describing the flow on the center manifold is derived
Contents 1. Introduction
2. Two delays and no self-connections
3. A network with self-connections and one delay
4. A pure imaginary pair and z zero as simple eigenvalues
Key words
Mathmatical Subject Classification