Controlling Mackey-Glass chaos

Gábor Kiss, Gergely Röst*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


The Mackey-Glass equation is the representative example of delay induced chaotic behavior. Here, we propose various control mechanisms so that otherwise erratic solutions are forced to converge to the positive equilibrium or to a periodic orbit oscillating around that equilibrium. We take advantage of some recent results of the delay differential literature, when a sufficiently large domain of the phase space has been shown to be attractive and invariant, where the system is governed by monotone delayed feedback and chaos is not possible due to some Poincarë-Bendixson type results. We systematically investigate what control mechanisms are suitable to drive the system into such a situation and prove that constant perturbation, proportional feedback control, Pyragas control, and state dependent delay control can all be efficient to control Mackey-Glass chaos with properly chosen control parameters.

Original languageEnglish
Article number114321
Issue number11
Early online date26 Oct 2017
Publication statusPublished - 01 Nov 2017
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics


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