Pseudospectral discretization of nonlinear delay equations: New prospects for numerical bifurcation analysis

D. Breda, O. Diekmann, M. Gyllenberg, F. Scarabel, R. Vermiglio

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

We apply the pseudospectral discretization approach to nonlinear delay models described by delay differential equations, renewal equations, or systems of coupled renewal equations and delay differential equations. The aim is to derive ordinary differential equations and to investigate the stability and bifurcation of equilibria of the original model by available software packages for continuation and bifurcation for ordinary differential equations. Theoretical and numerical results confirm the effectiveness and the versatility of the approach, opening a new perspective for the bifurcation analysis of delay equations, in particular coupled renewal and delay differential equations.

Original languageEnglish
Pages (from-to)1-23
Number of pages23
JournalSIAM Journal on Applied Dynamical Systems
Volume15
Issue number1
DOIs
Publication statusPublished - 2016

Keywords

  • Delay differential equations
  • Numerical bifurcation
  • Physiologically structured populations
  • Pseudospectral method
  • Renewal equations
  • Stability of equilibria
  • Volterra delay equations

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