Oscillations in multi-stable monotone systems with slowly varying feedback

Tomáš Gedeon, Eduardo D. Sontag

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


The study of dynamics of gene regulatory networks is of increasing interest in systems biology. A useful approach to the study of these complex systems is to view them as decomposed into feedback loops around open loop monotone systems. Key features of the dynamics of the original system are then deduced from the input-output characteristics of the open loop system and the sign of the feedback. This paper extends these results, showing how to use the same framework of input-output systems in order to prove existence of oscillations, if the slowly varying strength of the feedback depends on the state of the system.

Original languageAmerican English
Pages (from-to)273-295
Number of pages23
JournalJournal of Differential Equations
Issue number2
StatePublished - Aug 15 2007

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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