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Slowly oscillating periodic solutions for a delayed frustrated network of two neurons. (English) Zbl 0998.34058

Here, the authors discuss the dynamics for a network of two neurons with negative feedback of the form

x ˙(t)=-μ 1 x(t)+F(y(t-τ 1 ))+I 1 ,y ˙(t)=-μ 2 y(t)-G(x(t-τ 2 ))+I 2 ,

where μ 1 >0,μ 2 >0,τ 1 0,τ 2 0 are constants, τ 1 +τ 2 >0, I 1 and I 2 are constants, F and G are bounded C 1 -functions with F ' (ξ)>0,G ' (ξ)>0. The authors show a two-dimensional closed disk bordered by a slowly oscillating periodic orbit. A description on the dynamics of the flow restricted to this closed disk is given. This paper is related to the authors work [Existence and attraction of a phase-locked oscillation in a delayed network of two neurons (to appear)].

MSC:
34K13Periodic solutions of functional differential equations
92B20General theory of neural networks (mathematical biology)
68M10Network design and communication of computer systems