Differential and Integral Equations

Stable periodic motion of a system with state dependent delay

Hans-Otto Walther

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We consider an autonomous system of a differential and a functional equation for one-dimensional motion of an object which attempts to regulate its distance from a given point by means of reflected signals. In a suitable, compact state space the forward initial value problem is well-posed. For certain configurations of the parameters involved we prove that there exist periodic orbits which are exponentially stable with asymptotic phase.

Article information

Differential Integral Equations, Volume 15, Number 8 (2002), 923-944.

First available in Project Euclid: 21 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 34K13: Periodic solutions
Secondary: 34K20: Stability theory 37C27: Periodic orbits of vector fields and flows


Walther, Hans-Otto. Stable periodic motion of a system with state dependent delay. Differential Integral Equations 15 (2002), no. 8, 923--944. https://projecteuclid.org/euclid.die/1356060779

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