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Invariant set and attractivity of nonlinear differential equations with delays. (English) Zbl 1023.34066

The authors discuss the invariant set, the attracting set, and the basin of attraction of nonlinear and nonautonomous delay differential equations

y ˙(t)=-Ay(t)+F(t,y t )+q(t),A=diag{a i }·

Such equation can be seen as a generalization of the neural network models. Some sufficient conditions are obtained for the existence of an attracting set and the basin of attraction. The approach is to employ the variation of constants formula. Two examples are given to explain the results.

MSC:
34K19Invariant manifolds (functional-differential equations)
34K20Stability theory of functional-differential equations
92B20General theory of neural networks (mathematical biology)