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Stability criteria for a class of linear differential equations with off-diagonal delays. (English) Zbl 1180.34082
This paper is concerned with the following delay differential system with off-diagonal delays \begin{aligned} x_1'(t)&= a_1x_1(t)+ b_1x_n(t-r_1),\\ x_2'(t)&= -a_2x_2(t)+b_2x_1(t-r_2),\\ & \qquad\vdots\\ x_n'(t)&= -a_nx_n(t)+b_nx_n(t-r_n),\end{aligned} where $$a_j, b_j$$ are real numbers and $$r_j$$ nonnegative real numbers for $$j=1,2,\dots,n$$. By means of root-analysis of the characteristic equation of the above system the authors obtain criteria for the asymptotic stability of the zero solution of the system.

##### MSC:
 34K20 Stability theory of functional-differential equations 34K06 Linear functional-differential equations
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