Journal of Dynamics and Differential Equations

, Volume 23, Issue 4, pp 727–790 | Cite as

Large-Amplitude Periodic Solutions for Differential Equations with Delayed Monotone Positive Feedback



The aim of this paper is to show that the structure of the global attractor for delayed monotone positive feedback can be more complicated than the union of spindle-like structures between consecutive stable equilibria with respect to the pointwise ordering. Large amplitude periodic orbits—in the sense that they are not between two consecutive stable equilibria—are constructed for nonlinearities close to a step function. For some nonlinearities there are exactly two large amplitude periodic orbits. By describing the unstable sets of these periodic orbits, a complete picture is obtained about the global attractor outside the spindle-like structures.


Delay differential equation Positive feedback Periodic orbit Large amplitude Discrete Lyapunov functional Hyperbolicity Return map Heteroclinic orbit 

Mathematics Subject Classification (2000)

34K13 37D05 37L25 37L45 


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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Bolyai InstituteUniversity of SzegedSzegedHungary
  2. 2.Analysis and Stochastic Research Group of the Hungarian Academy of SciencesUniversity of SzegedSzegedHungary

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