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DY: Fachverband Dynamik und Statistische Physik
DY 15: Nonlinear Dynamics, Synchronization, Chaos I
DY 15.6: Talk
Monday, March 12, 2018, 16:45–17:00, BH-N 128
Synchronization of high dimensional systems using an ensemble approximation of the inverse linearized delay coordinates map — Flavia R. Pinheiro1, Peter Jan van Leeuwen1, and •Ulrich Parlitz2 — 1Dept. of Meteorology, University of Reading, UK and the National Centre for Earth Observation (NCEO) — 2Max Planck Institute for Dynamics and Self-Organization, Göttingen
Synchronization of uni-directly coupled systems can be significantly improved by using delay reconstruction of states in the coupling term [1], [2]. This approach, however, requires the computation and (pseudo) inversion of the Jacobian matrix of the delay coordinates map which is for high dimensional systems computationally extremely expensive. As an alternative, we present a method for approximating the required Jacobian matrix using an ensemble approach [3]. The feasibility and efficacy of this coupling scheme is demonstrated for D-dimensional Lorenz-96 systems with D ranging from 20 to 1000. With its capability to achieve synchronization of high dimensional systems this approach may serve as a building block of novel data assimilation schemes (nonlinear particle filters) [3].
[1] D. Rey et al.. Phys. Lett. A. 378, 869-873 (2014) DOI: 10.1016/j.physleta.2014.01.027
[2] D. Rey et al., Phys. Rev. E. 90: 062916 (2014) DOI: 10.1103/PhysRevE.90.062916
[3] F. R. Pinheiro, P. J. van Leeuwen, and U. Parlitz, to appear in Q. J. R. Meteorol. Soc., DOI: 10.1002/qj.3204