Software for Stability and Bifurcation Analysis of Delay Differential Equations and Applications to Stabilization

Abstract

DDE-BIFTOOL is a Matlab software package for the stability and bifurcation analysis of parameter-dependent systems of delay differential equations. Using continuation, branches of steady state solutions and periodic solutions can be computed. The local stability of a solution is determined by computing relevant eigenvalues (steady state solutions) or Floquet Multipliers (periodic solutions). Along branches of solutions, bifurcations can be detected and branches of fold or Hopf bifurcation points can be computcd. We outline the capabilities of the package and some of the numerical methods upon which it is based. We illustrate the usage of the package for the analysis of two model problems and we outline applications and extensions towards controller synthesis problems. We explain how its stability routines can be used for the implementation of the continuous pole placement method, which allows to solve stabilization problems where multiple parameters need to be tuned simultaneously.KeywordsPeriodic SolutionHopf BifurcationSteady State SolutionHomoclinic OrbitBifurcation AnalysisThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.