Nonlinear Dynamics at the Free University Berlin

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)
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