TY - JOUR
T1 - Coarse bifurcation diagrams via microscopic simulators
T2 - A state-feedback control-based approach
AU - Siettos, Constantinos I.
AU - Kevrekidis, Ioannis G.
AU - Maroudas, Dimitrios
N1 - Funding Information:
This work was partially supported by the AFOSR (Dynamics and Control) and an NSF-ITR grant (Award No. ACI-0205584). The authors are grateful to Prof. Alexei Makeev, of Moscow State University, for the stochastic simulation codes and for numerous fruitful discussions.
PY - 2004/1
Y1 - 2004/1
N2 - 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.
AB - 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.
KW - Arc-length continuation
KW - Bifurcation diagram
KW - Kinetic Monte Carlo
KW - Microscopic simulators
KW - State feedback control
KW - Time steppers
UR - http://www.scopus.com/inward/record.url?scp=3042713738&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=3042713738&partnerID=8YFLogxK
U2 - 10.1142/S0218127404009193
DO - 10.1142/S0218127404009193
M3 - Article
AN - SCOPUS:3042713738
SN - 0218-1274
VL - 14
SP - 207
EP - 220
JO - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
JF - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
IS - 1
ER -