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The European Physical Journal Special Topics

, Volume 191, Issue 1, pp 91–103 | Cite as

Complex dynamics in delay-differential equations with large delay

  • M. Wolfrum
  • S. Yanchuk
  • P. Hövel
  • E. Schöll
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Abstract.

We investigate the dynamical properties of delay differential equations with large delay. Starting from a mathematical discussion of the singular limit τ → ∞, we present a novel theoretical approach to the stability properties of stationary solutions in such systems. We introduce the notion of strong and weak instabilities and describe a method that allows us to calculate asymptotic approximations of the corresponding parts of the spectrum. The theoretical results are illustrated by several examples, including the control of unstable steady states of focus type by time delayed feedback control and the stability of external cavity modes in the Lang-Kobayashi system for semiconductor lasers with optical feedback.

Keywords

Periodic Solution European Physical Journal Special Topic Imaginary Axis Optical Feedback Large Delay 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© EDP Sciences and Springer 2011

Authors and Affiliations

  • M. Wolfrum
    • 1
  • S. Yanchuk
    • 2
  • P. Hövel
    • 3
  • E. Schöll
    • 3
  1. 1.Weierstrass Institute for Applied Analysis and StochasticsBerlinGermany
  2. 2.Institut für Mathematik, Humboldt-Universität zu BerlinBerlinGermany
  3. 3.Institut für Theoretische Physik, Technische Universität BerlinBerlinGermany

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