Detection of coarse-grained unstable states of microscopic/stochastic systems: A timestepper-based iterative protocol

Tsoumanis, AC; Siettos, CI

dc.contributor.author	Tsoumanis, AC	en
dc.contributor.author	Siettos, CI	en
dc.date.accessioned	2014-03-01T01:37:35Z
dc.date.available	2014-03-01T01:37:35Z
dc.date.issued	2012	en
dc.identifier.issn	0924-090X	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/21561
dc.subject	Bifurcation theory	en
dc.subject	Coarse timestepping	en
dc.subject	Complex systems	en
dc.subject	Large-scale systems	en
dc.subject	Nonlinear dynamics	en
dc.subject	Numerical detection of saddles	en
dc.subject.classification	Engineering, Mechanical	en
dc.subject.classification	Mechanics	en
dc.subject.other	Adaptive mechanism	en
dc.subject.other	Agent-based model	en
dc.subject.other	Bifurcation theory	en
dc.subject.other	Chord method	en
dc.subject.other	Coarse-grained	en
dc.subject.other	Complex dynamical systems	en
dc.subject.other	Iterative procedures	en
dc.subject.other	Kinetic Monte Carlo simulation	en
dc.subject.other	Large population	en
dc.subject.other	Macroscopic levels	en
dc.subject.other	Non-linear dynamics	en
dc.subject.other	Numerical detection of saddles	en
dc.subject.other	Open loops	en
dc.subject.other	Saddle node bifurcation	en
dc.subject.other	Saddle point	en
dc.subject.other	Surface-catalytic reaction	en
dc.subject.other	Time-stepping	en
dc.subject.other	Turning points	en
dc.subject.other	Unstable state	en
dc.subject.other	Bifurcation (mathematics)	en
dc.subject.other	Catalysis	en
dc.subject.other	Computer simulation	en
dc.subject.other	Dynamical systems	en
dc.subject.other	Dynamics	en
dc.subject.other	Large scale systems	en
dc.subject.other	Monte Carlo methods	en
dc.subject.other	Numerical methods	en
dc.subject.other	Partial differential equations	en
dc.subject.other	Surface reactions	en
dc.subject.other	Ordinary differential equations	en
dc.title	Detection of coarse-grained unstable states of microscopic/stochastic systems: A timestepper-based iterative protocol	en
heal.type	journalArticle	en
heal.identifier.primary	10.1007/s11071-011-9962-0	en
heal.identifier.secondary	http://dx.doi.org/10.1007/s11071-011-9962-0	en
heal.language	English	en
heal.publicationDate	2012	en
heal.abstract	We address an iterative procedure that can be used to detect coarse-grained hyperbolic unstable equilibria (saddle points) of microscopic simulators when no equations at the macroscopic level are available. The scheme is based on the concept of coarse timestepping (Kevrekidis et al. in Commun. Math. Sci. 1(4):715-762, 2003) incorporating an adaptive mechanism based on the chord method allowing the location of coarse-grained saddle points directly. Ultimately, it can be used in a consecutive manner to trace the coarse-grained open-loop saddle-node bifurcation diagrams of complex dynamical systems and large-scale systems of ordinary and/or partial differential equations. We illustrate the procedure through two indicative examples including (i) a kinetic Monte Carlo simulation (kMC) of simple surface catalytic reactions and (ii) a simple agent-based model, a financial caricature which is used to simulate the dynamics of buying and selling of a large population of interacting individuals in the presence of mimesis. Both models exhibit coarse-grained regular turning points which give rise to branches of saddle points. © 2011 Springer Science+Business Media B.V.	en
heal.publisher	SPRINGER	en
heal.journalName	Nonlinear Dynamics	en
dc.identifier.doi	10.1007/s11071-011-9962-0	en
dc.identifier.isi	ISI:000297544000008	en
dc.identifier.volume	67	en
dc.identifier.issue	1	en
dc.identifier.spage	103	en
dc.identifier.epage	117	en