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Asymptotically stable periodic solutions of delay equations with positive feedback

We investigate a nonlinear autonomous scalar retarded functional differential equation (RFDE) of first order containing a linear damping term and a nonlinearity that models positive feedback relative to the equilibrium solution $x=0$. It is known that in case of a monotone nonlinearity all periodic solutions of such a RFDE are unstable; we prove that this does not hold if the nonlinearity is not monotone, in particular we show existence of asymptotically stable periodic solutions.

Contacts:

Axel Schulze-Halberg, PD Dr. D. Stoffer, Prof. Dr. U. Kirchgraber

Electronic Contacts:

Axel Schulze-Halberg

Last Update:

16/07/99

Responsible:

Professor or Project Leader:           : Prof. Dr. Urs Kirchgraber
Institute or Independent Professorship : Independent Professorship of Mathematics
Department                             : Department of Mathematics

Comments to the ETH Research Report administration : Sat Jun 19 16:30:35 1999

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author Michele Marcionelli and design: Michele Marcionelli