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Stability in a three-dimensional system of delay-differential equations. (English) Zbl 0880.34075

The stability properties of the null solution of the three-dimensional linear system \(x'(t)=-x(t)+ Ax(t-\tau)\) are investigated. When all the diagonal entries of the matrix \(A\) are zero, the values of the parameters for which this solution is asymptotically stable are explicitly determined. The relation of this result to neural network models is discussed.
Reviewer: S.O.Londen (Espoo)

MSC:

34K20 Stability theory of functional-differential equations
92B20 Neural networks for/in biological studies, artificial life and related topics
34K25 Asymptotic theory of functional-differential equations
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