Linearized stability in periodic functional differential equations with state-dependent delays☆

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Abstract

In this paper, we study stability of periodic solutions of a class of nonlinear functional differential equations (FDEs) with state-dependent delays using the method of linearization. We show that a periodic solution of the nonlinear FDE is exponentially stable, if the zero solution of an associated linear periodic linear homogeneous FDE is exponentially stable.

Keywords

Linearization
State-dependent delay
Stability
Periodic solution

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This research was partially supported by Hungarian National Foundation for Scientific Research Grant No. T031935.

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