Periodic Solutions and Hydra Effect for Delay Differential Equations with Nonincreasing Feedback

• Tibor Krisztin ^[1] ; Mónika Polner ^[1] ; Gabriella Vas ^[1]
  1. [1] University of Szeged

     University of Szeged

     Hungría

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 16, Nº 2, 2017, págs. 269-292
• Idioma: inglés
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• Resumen

  • We consider a delay differential equation modeling production and destruction, and prove the presence of the paradoxial hydra effect. Namely, for the equation y˙(t) = −μy(t) + f (y(t − 1)) with μ > 0 and nonincreasing f : R → (0,∞), it is shown that the mean value of certain solutions can be increased by increasing the value of the (destruction) parameter μ. The nonlinearity f in the equation is a step function or a smooth function close to a step function. This particular form of f allows us to construct periodic solutions, and to evaluate the mean values of the periodic solutions.

    Our result explains how the global form of the nonlinearity f (the production term) induces the appearance of the hydra effect.