Carryover of a Saddle-Node Bifurcation After Transforming a Parameter into a Variable

Carlos Contreras, Gustavo Carrero, Gerda de Vries

Research output: Contribution to journalJournal Articlepeer-review

Abstract

In this article, we introduce and study the carryover of a saddle-node bifurcation, a concept that describes how a saddle-node bifurcation of a dynamical system is carried over into an extended dynamical system obtained by transforming one of the parameters of the original system into a variable. We show that additional transversality and singularity conditions are needed to guarantee the carryover of a saddle-node bifurcation and provide a graphical methodology with a two-parameter bifurcation diagram to verify that such conditions are met. The results are applied to a gene activation model when the parameter describing the signal for activation is transformed into a variable, and to a cell cycle regulatory model when the parameter describing the cell mass is transformed into a variable. In both cases, we show that a saddle-node bifurcation carryover takes place.

Original languageEnglish
JournalJournal of Dynamics and Differential Equations
DOIs
Publication statusAccepted/In press - 2021

Keywords

  • Bifurcation
  • Bifurcation diagram
  • Mathematical modeling
  • Parameter transformation
  • Saddle-node bifurcation

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