Delay and periodicity

S. Yanchuk and P. Perlikowski
Phys. Rev. E 79, 046221 – Published 29 April 2009

Abstract

Systems with time delay play an important role in modeling of many physical and biological processes. In this paper we describe generic properties of systems with time delay, which are related to the appearance and stability of periodic solutions. In particular, we show that delay systems generically have families of periodic solutions, which are reappearing for infinitely many delay times. As delay increases, the solution families overlap leading to increasing coexistence of multiple stable as well as unstable solutions. We also consider stability issue of periodic solutions with large delay by explaining asymptotic properties of the spectrum of characteristic multipliers. We show that the spectrum of multipliers can be split into two parts: pseudocontinuous and strongly unstable. The pseudocontinuous part of the spectrum mediates destabilization of periodic solutions.

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  • Received 22 January 2009

DOI:https://doi.org/10.1103/PhysRevE.79.046221

©2009 American Physical Society

Authors & Affiliations

S. Yanchuk1 and P. Perlikowski1,2

  • 1Institute of Mathematics, Humboldt University of Berlin, Unter den Linden 6, 10099 Berlin, Germany
  • 2Division of Dynamics, Technical University of Lodz, Stefanowskiego 1/15, 90-924 Lodz, Poland

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Issue

Vol. 79, Iss. 4 — April 2009

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