Monotonicity of the Poincaré Mapping in Some Models of Circular Gene Networks

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Abstract

We obtain some sufficient conditions for the existence of a periodic trajectory of the Elowitz-Leibler type piecewise linear dynamical system that simulates a simplest nonsymmetric circular gene network. We prove the monotonicity of the corresponding Poincaré mapping and construct an invariant toric neighborhood of this cycle.

Original languageEnglish
Pages (from-to)472-479
Number of pages8
JournalJournal of Applied and Industrial Mathematics
Volume13
Issue number3
DOIs
Publication statusPublished - 1 Jul 2019

Keywords

  • circular gene network
  • cycle
  • invariant domain
  • piecewise-linear dynamical system
  • Poincaré mapping
  • positive and negative feedbacks

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