Abstract
We consider a system of delay differentialequations$\dot x_i(t)=F_i(x_1(t),\ldots,x_n(t),t)-$ sign $x_i(t-h_i),\quad i=1,\ldots,n,$with positive constant delays $h_1,...,h_n$ and perturbations$F_1,...,F_n$ absolutely bounded by a constant less than 1. Thisis a model of a negative feedback controller of relay typeintended to bring the system to the origin. Non-zero delays do notallow such a stabilization, but cause oscillations around zerolevel in any variable. We introduce integral-valued relativefrequencies of zeroes of the solution components, and show thatthey always decrease to some limit values. Moreover, for anyprescribed limit relative frequencies, there exists at least an$n$-parametric family of solutions realizing these oscillationfrequencies. We also find sufficient conditions for the stabilityof slow oscillations, and show that in this case there existabsolute frequencies of oscillations.
Published Version
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