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

Research Project

Design of self-organizing spatio-temporal patterns

Research director

Prof. Dr. Bernold Fiedler

Members

PD Dr. Pavel Gurevich

PD Dr. Stefan Liebscher

Dr. Abderrahim Azouani (associated member)

Dr. Sergey Tikhomirov (associated member)

Isabelle Schneider

Matthias Bosewitz

Summary

The project aims at the design of self-organizing structures with prescribed

• temporal dynamics,
• spatial patterns, and
• spatio-temporal patterns.

We plan to explore the possibilities of endowing given systems with appropriate spatial and temporal feedback controls to achieve such prescribed behavior. Specific applied contexts for the above aims arise in coupled neural or molecular networks, semiconductor nanostructures, and chemical reaction-diffusion systems. The project aims far beyond state-of-the-art modelling or compilations of the resulting spatial and temporal phenomena like Turing patterns, pattern recognition by neural networks of spin-glass type, or spirals, meanders, and scrolls in reactive and diffusive media. It is the active design of prescribed spatio-temporally coherent behavior which is the principal focus here. Time-delayed feedback and hysteresis models with their resulting nonlinear dynamics of ordinary and partial differential delay equations will play a major role in the project. In particular, we will use methods from bifurcation theory, equivariant bifurcation theory, and functional differential equations.

Preprints and Publications

A. Mochizuki, B. Fiedler

Sensitivity of chemical reaction networks: a structural approach. 1. Examples and the carbon metabolic network.
Submitted 2014.
(pdf, 542 kB)

B. Fiedler, A. Mochizuki

Sensitivity of chemical reaction networks: a structural approach. 2. Regular monomolecular systems.
Submitted 2014.
(pdf, 343 kB)

B. Fiedler, A. Mochizuki, G. Kurosawa, D. Saito

Dynamics and control at feedback vertex sets. I: Informative and determining nodes in regulatory networks.
J. Dyn. Differ. Equations 25 (2013), 563-604.
(pdf, 4.041 kB)

A. Mochizuki, B. Fiedler, G. Kurosawa, D. Saito

Dynamics and control at feedback vertex sets. II: A faithful monitor to determine the diversity of molecular activities in regulatory networks.
J. Theor. Biol. 335 (2013), 130-146.
(pdf, 5.253 kB)

S.-B. Hsu, B. Fiedler, H.-H. Lin

Classification of potential flows under renormalization group transformation.
Submitted 2014.
(pdf, 107 kB)

Isabelle Schneider, Matthias Bosewitz

Eliminating restrictions of time-delayed feedback control using equivariance
Accepted DCDS-A (2014).
(pdf, 410 kB)

A. Zakharova, I. Schneider, Y. N. Kyrychko, K. B. Blyuss, A. Koseska, B. Fiedler and E. Schöll

Time delay control of symmetry-breaking primary and secondary oscillation death
Europhys. Lett. 104 (2013), 50004.
(pdf, 950 kB)

I. Schneider

Equivariant Pyragas control
Master Thesis, Free University Berlin, 2014.
(pdf, 1.8 MB)

M. Bosewitz

Stabilisierung gekoppelter Oszillatoren durch verzögerte Rückkopplungskontrolle
Bachelor Thesis, Free University Berlin, 2013.
(pdf, 482 kB)

K. Bubolz

Stabilisierung periodischer Orbits im System zweier gekoppelter Oszillatoren durch zeitverzögerte Rückkopplungskontrolle
Bachelor Thesis, Free University Berlin, 2013.
(pdf, 961 kB)

I. Schneider

Oscillation suppression in nonlinear coupled oscillators with and without time delay
Bachelor Thesis Physics, Free University Berlin, SFB 910, 2013.
(pdf, 300 kB)

I. Schneider

Delayed feedback control of three diffusively coupled Stuart-Landau oscillators: a case study in equivariant Hopf bifurcation
Philosophical Transactions of the Royal Society A, Theme Issue "Dynamics, control and information in delay-coupled systems" (2013).
(pdf, 3.4 MB)

I. Schneider

Stabilisierung von drei symmetrisch gekoppelten Oszillatoren durch zeitverzögerte Rückkopplungskontrolle
Bachelor Thesis, Free University of Berlin, 2011.
(pdf, 1.2 MB)

P. Gurevich, D. Rachinskii

Well-posedness of parabolic equations containing hysteresis with diffusive thresholds.
Proceedings of the Steklov Institute of Mathematics.Vol. 283 (2013). P. 87-109.
(pdf)

G. Friedman, P. Gurevich, S. McCarthy, D. Rachinskii

Switching behaviour of two-phenotype bacteria in varying environment.
J. Physics: Conference Series. Accepted for publication.
(pdf)

P.L. Gurevich, S.B. Tikhomirov

Systems of reaction-diffusion equations with spatially distributed hysteresis.
Mathematica Bohemica (Proc. Equadiff 2013). Accepted.
(pdf)

P.L. Gurevich, R.V. Shamin, S.B. Tikhomirov

Reaction-diffusion equations with spatially distributed hysteresis.
SIAM J. Math. Anal. Vol. 45, No. 3 (2013). P. 1328-1355.
(pdf)

P.L. Gurevich, S.B. Tikhomirov

Uniqueness of transverse solutions for reaction-diffusion equations with spatially distributed hysteresis.
Nonlinear Analysis. Vol. 75 (2012). P. 6610-6619.
(pdf)

P.L. Gurevich, S.B. Tikhomirov

Symmetric periodic solutions of parabolic problems with discontinuous hysteresis.
Journal of Dynamics and Differential Equations. Vol. 23. No. 4. (2011). P. 923-960.
(pdf)

P.L. Gurevich

Periodic solutions of parabolic problems with hysteresis on the boundary.
Discrete Cont. Dynam. Systems. Series A. Volume 29, Number 3 (2011) P. 1041-1083.
(pdf)