Periodic Solutions and Hydra Effect for Delay Differential Equations with Nonincreasing Feedback
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Tibor Krisztin [1] ; Mónika Polner [1] ; Gabriella Vas [1]
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[1] University of Szeged
University of Szeged
Hungría
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- 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.
