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 for partial differential equations
Patterns of Dynamics (Gurevich, Hell, Sandstede, Scheel, eds.), Springer Proceedings in Mathematics & Statistics Volume 205 (2018).
(pdf, 577 kB)

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)

B. Fiedler, I. Schneider

Stabilized rapid oscillations in a delay equation: Feedback control by a small resonant delay.
in press, Discrete and Continuous Dynamical Systems - Series S (2018).
(pdf, 2.310 kB)
arxiv.org/abs/1708.08101

A. Röhm, K. Lüdge, I. Schneider

Bistability in Two Simple Symmetrically Coupled Oscillators with Symmetry-broken Amplitude-and Phase-Locking
Chaos: An Interdisciplinary Journal of Nonlinear Science 28 (6) , 063114 (2018)
arxiv.org/abs/1712.01610