TY - JOUR
T1 - A trajectory-free framework for analysing multiscale systems
AU - Froyland, Gary
AU - Gottwald, Georg Arnold
AU - Hammerlindl, Andy
PY - 2016
Y1 - 2016
N2 - We develop algorithms built around properties of the transfer operator and Koopman operator which (1) test for possible multiscale dynamics in a given dynamical system, (2) estimate the magnitude of the time-scale separation, and finally (3) distill the reduced slow dynamics on a suitably designed subspace. By avoiding trajectory integration, the developed techniques are highly computationally efficient. We corroborate our findings with numerical simulations of a test problem.
AB - We develop algorithms built around properties of the transfer operator and Koopman operator which (1) test for possible multiscale dynamics in a given dynamical system, (2) estimate the magnitude of the time-scale separation, and finally (3) distill the reduced slow dynamics on a suitably designed subspace. By avoiding trajectory integration, the developed techniques are highly computationally efficient. We corroborate our findings with numerical simulations of a test problem.
KW - Koopman operator
KW - Model reduction
KW - Multiscale dynamics
KW - Transfer operator
UR - http://www.scopus.com/inward/record.url?scp=84975468950&partnerID=8YFLogxK
UR - http://ac.els-cdn.com.ezproxy.lib.monash.edu.au/S0167278916301646/1-s2.0-S0167278916301646-main.pdf?_tid=ccc46ce8-db87-11e6-8609-00000aacb35e&acdnat=1484528878_e6f15965e3ec5ebb8aa116b8c8aad8dd
U2 - 10.1016/j.physd.2016.04.010
DO - 10.1016/j.physd.2016.04.010
M3 - Article
SN - 0167-2789
VL - 328-329
SP - 34
EP - 43
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
ER -