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

Content Provider	Springer Nature Link
Author	Tsoumanis, A. C. Siettos, C. I.
Copyright Year	2011
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.
Starting Page	103
Ending Page	117
Page Count	15
File Format	PDF
ISSN	0924090X
Journal	Nonlinear Dynamics
Volume Number	67
Issue Number	1
e-ISSN	1573269X
Language	English
Publisher	Springer Netherlands
Publisher Date	2011-02-12
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Nonlinear dynamics Bifurcation theory Numerical detection of saddles Large-scale systems Complex systems Coarse timestepping Mechanical Engineering Vibration, Dynamical Systems, Control Automotive Engineering Mechanics
Content Type	Text
Resource Type	Article
Subject	Ocean Engineering Applied Mathematics Control and Systems Engineering Mechanical Engineering Electrical and Electronic Engineering Aerospace Engineering

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