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Stability of simple periodic solutions of neutral functional differential equations. (English) Zbl 1028.34068
The authors study the stability of a simple periodic solution to an autonomous neutral functional-differential equation (NFDE) of the form \(dD(x_t)/dt=f(x_t)\). 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 to the equation above is asymptotically orbital stable with asymptotic phase. The used technique overcomes the difficulty that the solution operator of a NFDE does not smooth as \(t\) increases.

MSC:
34K20 Stability theory of functional-differential equations
34K40 Neutral functional-differential equations
34K13 Periodic solutions to functional-differential equations
34K19 Invariant manifolds of functional-differential equations
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