Stability of attractivity regions for autonomous functional differential equations

Abstract

We consider attractivity regions of the zero solutions of autonomous retarded functional differential equations (FDEs). It is shown that the attractivity region remains unchanged if the FDE undergoes a small perturbation in certain classes of FDEs. Especially we obtain the openness of the set of parameters α∈(0,π/2) such that the attractivity region of the equation\(\dot x(t) = - \alpha x(t - 1)[1 + x(t)]\) is given by the set of continuous functions ϕ:[−1,0] → R with ϕ(0)>−1.