Stability of simple periodic solutions of neutral functional differential equations

Abstract

We study the stability property of a simple periodic solution of an au- tonomous neutral functional dieren tial equation (NFDE) of the form d dt D(xt) = f(xt). A new proof based on local integral manifold theory and the implicit function theorem is given for the classical result that a simple periodic orbit of the equation above is asymptotically orbitally stable with asymptotic phase. The technique used overcomes the dicult y that the solution operator of a NFDE does not smooth as t increases.