Structure of the global attractor of cyclic feedback systems

Tomáš Gedeon, Konstantin Mischaikow

Research output: Contribution to journalArticlepeer-review

24 Scopus citations


We characterize the dynamics on global attractors of cyclic feedback systems. Under mild restrictions the description is given in terms of a semiconjugacy to a simple model system which possesses Morse-Smale dynamics. However, for the completely general case, no simple model system is feasible and hence we introduce a weaker notion of equivalence, namely, topological semiequivalency. We then prove that the global attractor of a cyclic feedback system is topologically semiequivalent to the original model flow. Main ingredients in the proof are the discrete Lyapunov function introduced by Mallet-Paret and Smith and the Conley index theory.

Original languageEnglish (US)
Pages (from-to)141-190
Number of pages50
JournalJournal of Dynamics and Differential Equations
Issue number1
StatePublished - Jan 1995
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis


  • Conley index theory
  • Cyclic feedback system
  • Lyapunov function
  • global dynamics


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