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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