On Uniqueness of a Cycle in One Circular Gene Network Model

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Abstract

We obtain conditions for uniqueness of a cycle in the phase portraitof a piecewise linear dynamical systemof the Elowitz–Leibler typewhich simulates the functioning of a simplest circular gene network.We describe the behavior of trajectories of this systemin the invariant toric neighborhood of the cycle.

Original languageEnglish
Pages (from-to)79-86
Number of pages8
JournalSiberian Mathematical Journal
Volume63
Issue number1
DOIs
Publication statusPublished - Jan 2022

Keywords

  • 514.745.82
  • block-linear dynamical system
  • circular gene network
  • cycle
  • fixed point
  • invariant domain
  • Poincaré map
  • positive and negative feedbacks

OECD FOS+WOS

  • 1.01 MATHEMATICS

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