Nonlinear Dynamics at the Free University Berlin

DFG Collaborative Research Center 910 on
Control of self-organizing nonlinear systems

Research Project

Spatio-temporal patterns: observation, control, and design

Research director
Prof. Dr. Bernold Fiedler
Members
Ignacio González
Dr. Isabelle Schneider
Fustel Soh Nzokou
Nicola Vassena

Summary

Our goal is a new qualitatively oriented approach to the observation, the open-loop and feedback control, and ultimately the rational design of spatio-temporal patterns of applied relevance. Mathematical topics include differential equations on graphs, as well as partial and delayed differential equations. Applications include gene regulatory and metabolic networks. Specifically we plan to address three areas:

  1. qualitative analysis of network sensitivity;
  2. observation and control of regulatory networks;
  3. rational design of spatio-temporal dynamics.


Preprints and Publications

B. Fiedler, A. Mochizuki
Sensitivity of chemical reaction networks: a structural approach. 1. Examples and the carbon metabolic network.
Journal of Theoretical Biology, Volume 367, 21 February 2015, pp. 189–202.
(pdf, 542 kB)
B. Fiedler, A. Mochizuki
Sensitivity of chemical reaction networks: a structural approach. 2. Regular monomolecular systems.
Mathematical Methods in the Applied Sciences, Volume 38, 15 November 2015, pp. 3519-3537.
(pdf, 393 kB)
B. Fiedler, S. M. Oliva
Delayed feedback control of a delay equation at Hopf bifurcation.
Submitted 2015.
(pdf, 2.659 kB)
B. Fiedler, M. Kapeller, S. Loos, I. Schneider, E. Schöll., A. Zakharova
Stable and transient multi-cluster oscillation death in nonlocally coupled networks
Phys. Rev. E 92, 052915 (2015).
(pdf, 600 kB)
Matthias Bosewitz, Isabelle Schneider
Eliminating restrictions of time-delayed feedback control using equivariance.
Discrete and Continuous Dynamical Systems Series A 36 (1), 451-467 (2016).
(pdf, 410 kB)
Bernold Fiedler, Isabelle Schneider
Symmetry-breaking control of rotating waves
In: "Control of Self-Organizing Nonlinear Systems", Springer-Verlag, 2016, pp. 105-126.
(pdf, 2,9 MB)
Bernhard Brehm, Bernold Fiedler
Sensitivity of chemical reaction networks: a structural approach 3. Regular multimolecular systems.
submitted (2016).
(pdf, 1 MB)
Nicola Vassena
Monomolecular reaction networks: a new proof of flux transitivity
Master Thesis, Freie Universität Berlin (2016).
(pdf, 1.8 MB)
Isabelle Schneider
Spatio-temporal feedback control of partial differential equations
Dissertation, Free University Berlin, 2016.
auf dem Dissertationenserver der FU Berlin
Isabelle Schneider
An introduction to the control triple method
submitted (2016).
(pdf, 577kB)
Sascha Siegmund
Flux sensitivity analysis in chemical reaction networks
Master Thesis, Free University Berlin, 2016.
(pdf, 712 KB)
Alejandro López Nieto
Heteroclinic connections in delay equations
Master Thesis, Freie Universität Berlin, 2017.
(pdf)
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