Coarse bifurcation diagrams via microscopic simulators: A state-feedback control-based approach

Constantinos I. Siettos, Ioannis G. Kevrekidis, Dimitrios Maroudas

Research output: Contribution to journalArticlepeer-review

25 Scopus citations


We present and illustrate a feedback control-based framework that enables micro-scopic/stochastic simulators to trace their "coarse" bifurcation diagrams, characterizing the dependence of their expected dynamical behavior on parameters. The framework combines the so-called "coarse time stepper" and arc-length continuation ideas from numerical bifurcation theory with linear dynamic feedback control. An augmented dynamical system is formulated, in which the bifurcation parameter evolution is linked with the microscopic simulation dynamics through feedback laws. The augmentation stably steers the system along both stable and unstable portions of the open-loop bifurcation diagram. The framework is illustrated using kinetic Monte Carlo simulations of simple surface reaction schemes that exhibit both coarse regular turning points and coarse Hopf bifurcations.

Original languageEnglish (US)
Pages (from-to)207-220
Number of pages14
JournalInternational Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Issue number1
StatePublished - Jan 2004

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Engineering (miscellaneous)
  • General
  • Applied Mathematics


  • Arc-length continuation
  • Bifurcation diagram
  • Kinetic Monte Carlo
  • Microscopic simulators
  • State feedback control
  • Time steppers


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