Nonlinear Dynamics at the Free University Berlin

Prof. Dr. Bernold Fiedler


Research interests

Address:
Freie Universität Berlin
Institut für Mathematik
Arnimallee 3
D - 14195 Berlin
Office:
134, Arnimallee 7, rear building
Phone:
+ 49 - 30 - 838 75411
E-mail:
fiedler at math.fu-berlin.de
(replace the "at" by a @)

Preprints and Publications

B. Fiedler
Ein Räuber-Beute System mit zwei time-lags
Diploma Thesis, Heidelberg, 1980.
B. Fiedler
Stabilitätswechsel und globale Hopf-Verzweigung
PhD Thesis, Heidelberg, 1983
B. Fiedler
Global Hopf bifurcation in porous catalysts
in Equadiff 82, Knobloch & Schmitt (eds.), Lect. Notes Math. 1017, Springer-Verlag, Berlin 1983, 177-183.
B. Fiedler
An index for global Hopf bifurcation in parabolic systems
J. reine angew. Math. 359(1985), 1-36.
B. Fiedler
Multiplicity-induced oscillations in porous catalysts
in Temporal Order, Rensing & Jäger (eds.)
Springer-Verlag, Berlin 1985, 57-58.
A.J. Bremermann, B. Fiedler
On the stability of polymorphic host-pathogen populations
J. Theor. Biology 117(1985), 621-631.
B. Fiedler
Global Hopf bifurcation for Volterra integral equations
SIAM J. Math. Analysis 17(1986), 911-932.
P. Brunovsky, B. Fiedler
Simplicity of zeros in scalar parabolic equations
J. Diff. Eq. 62(1986), 237-241.
P. Brunovsky, B. Fiedler
Numbers of zeros on invariant manifolds in reaction diffusion equations
Nonlin. Analysis TMA 10(1986), 179-194.
B. Fiedler
Global Hopf bifurcation of two parameter flows
Arch. Rational Mech. Analysis 94(1986), 59-81.
P. Brunovsky, B. Fiedler
Connecting orbits in scalar reaction diffusion equations with Neumann boundary conditions
Equadiff 6, Vosmansky & Zlamal (eds.)
Lect. Notes Math. 1192, Springer-Verlag, Berlin 1986, 123-128.
B. Fiedler, A. Vanderbauwhede (eds.)
Symmetry and Dynamics
Workshop Heidelberg 1986, SFB 123, preprint 400.
P. Deuflhard, B. Fiedler, P. Kunkel
Efficient numerical pathfollowing beyond critical points
SIAM J. Numer. Analysis 24(1987), 912-927.
B. Fiedler
Heteroclinic connections of stationary solutions of scalar reaction diffusion equations
in Partial Differential Equations, Banach Center Publ. vol. 19, Bojarski (ed.) Warszawa 1987, 39-47.
P. Deuflhard, B. Fiedler, P. Kunkel
Efficient numerical pathfollowing beyond critical points in ODE models
in Large Scale Scientific Computing, Deuflhard & Engquist (eds.), Birkhäuser, Boston 1987, 97-113.
B. Fiedler
Global Hopf bifurcation in reaction diffusion systems with symmetry
in Dynamics of Infinite Dimensional Systems, Chow & Hale (eds.)
Springer-Verlag, Berlin 1987, 81-104.
B. Fiedler, P. Kunkel
Multistability, scaling, and oscillations
in Complex Chemical Reaction Systems, Warnatz & Jäger (eds.)
Springer-Verlag, Heidelberg 1987, 169-180.
B. Fiedler, P. Kunkel
A quick multiparameter test for periodic solutions
in Bifurcation: Analysis, Algorithms, Applications, Küpper & Seydel & Troger (eds.)
Birkhäuser Verlag, Basel 1987, 61-70.
P. Brunovsky, B. Fiedler
Connecting orbits in scalar reaction diffusion equations
Dynamics Reported 1(1988), 57-89.
S. Angenent, B. Fiedler
The dynamics of rotating waves in scalar reaction diffusion equations
Trans. AMS 307(1988), 545-568.
(journal, pdf)
B. Fiedler
Global Bifurcation of Periodic Solutions with Symmetry
Lect. Notes Math. 1309, Springer-Verlag, Heidelberg 1988.
B. Fiedler, J. Mallet-Paret
Connections between Morse sets for delay-differential equations
J. reine angew. Math. 397(1989), 23-41.
J.C. Alexander, B. Fiedler
Global decoupling of coupled symmetric oscillators
in Differential Equations, Dafermos & Ladas & Papanicolaou (eds.)
Marcel Dekker Inc., New York 1989, 7-16.
B. Fiedler
Discrete Ljapunov functionals and w-limit sets
Math. Modelling Numer. Analysis 23(1989), 415-431.
B. Fiedler, J. Mallet-Paret
The Poincare-Bendixson theorem for scalar reaction diffusion equations
Arch. Rational Mech. Analysis 107(1989), 325-345.
P. Brunovsky, B. Fiedler
Connecting orbits in scalar reaction diffusion equations II: the complete solution
J. Diff. Eq. 81(1989), 106-135.
S.-N. Chow, B. Deng, B. Fiedler
Homoclinic bifurcation at resonant eigen-values
J. Dynamics and Diff. Eq. 2 (1990), 177-244.
B. Fiedler, P. Polacik
Complicated dynamics of one-dimensional reaction diffusion equations with a non-local term
Proc. Royal Soc. Edinburgh 115A(1990), 167-192.
A. Schuppert, B. Fiedler
Thermisch stabiles Upscaling exothermer Reaktionen
Technical Report, Hoechst AG 1991.
B. Fiedler, K. Mischaikow
Dynamics of bifurcations for variational problems with O(3) equivariance: a Conley index approach
Arch. Rat. Mech. Anal. 119(1992), 145-196.
A. Vanderbauwhede, B. Fiedler
Homoclinic period blow-up in reversible and conservative systems
Z. angew. Math. Phys. 43(1992), 292-318.
B. Sandstede, B. Fiedler
Dynamics of periodically forced parabolic equations on the circle
J. Erg. Th. Dyn. Syst. 12(1992), 559-571.
B. Fiedler
Global attractors of one-dimensional parabolic equations: sixteen examples
Tatra Mountains Math. Publ. 4(1994), 67-92.
B. Fiedler, J. Scheurle
Discretization of Homoclinic Orbits and Invisible Chaos
Memoirs Amer. Math. Soc. 570, 1996.
G. Dangelmayr, B. Fiedler, K. Kirchgässner, A. Mielke
Dynamics of Nonlinear Waves in Dissipative Systems: Reduction, Bifurcation, and Stability
Pitman Res. Notes Math., Addison Wesley, 352, 1996.
B. Fiedler
Global pathfollowing of homoclinic orbits in two-parameter flows
Pitman Res. Notes Math. 352 (1996), 79-146
(gziped postscript, 784 kB)     (pdf, 812 kB)
B. Fiedler, S. Heinze
Homotopy invariants of time reversible periodic orbits I: Theory
J. Diff. Eq. 126(1996), 184-203.
B. Fiedler, S. Heinze
Homotopy invariants of time reversible periodic orbits II: Applications
J. Diff. Eq. 126(1996), 204-223.
C. Rocha, B. Fiedler
Heteroclinic orbits of semilinear parabolic equations
J. Diff. Eq. 125(1996), 239-281.
(gziped postscript, 452 kB)     (pdf, 324 kB)
B. Fiedler, D. Turaev
Coalescence of reversible homoclinic orbits causes elliptic resonance
Int. J. Bif. Chaos, 6(1996), 1007-1027.
(gziped postscript, 288 kB)     (pdf, 252 kB)
B. Fiedler
Do global attractors depend on boundary conditions?
Doc. Math. J. DMV 1(1996), 215-228.
M. Efendiev, B. Fiedler, A. Schuppert
Upscaling of some exothermic reactions from chemical industry
Z. Angew. Math. Mech. 76(1996) 153-156.
B. Fiedler, B. Sandstede, A. Scheel, C. Wulff
Bifurcation from relative equilibria of noncompact group actions: Skew products, meanders, and drifts
Doc. Math. J. DMV 1(1996), 479-505.
B. Fiedler, A. Schuppert, M. Efendiev
Thermisch stabiles Upscaling einer exothermen Modellreaktion
in Mathematik: Schlüsseltechnologie für die Zukunft, Hoffmann & Jäger & Lohmann & Schunck (eds.)
Springer-Verlag, Heidelberg, 1997, 83-90.
B. Fiedler, C. Rocha
Orbit equivalence of global attractors of semilinear parabolic differential equations
Trans. Amer. Math. Soc. 352(2000), 257-284.
(gziped postscript, 336 kB)     (pdf, 284 kB)
E. Behrends, B. Fiedler
Periods of discretized linear Anosov maps
Erg. Th. Dyn. Syst. 18(1998), 331-341.
(gziped postscript, 136 kB)     (pdf, 156 kB)
B. Fiedler, T. Gedeon
A class of convergent neural network dynamics
Physica D 111(1998), 288-294.
(gziped postscript, 472 kB)     (pdf, 164 kB)
B. Fiedler, T. Gedeon
A Lyapunov function for tridiagonal competitive-cooperative systems
SIAM J. Math. Analysis 30 (1999), 469-478.
(gziped postscript, 640 kB)     (pdf, 172 kB)
B. Fiedler, M. Belhaq, M. Houssni
Basins of attraction in strongly damped coupled mechanical oscillators: a global example
Z. Angew. Math. Phys. 50 (1999), 282-300 .
(gziped postscript, 640 kB)     (pdf, 236 kB)
M.A. Efendiev, B. Fiedler
Stable upscaling of exothermic reactor with several educts
Proc. Int. Symposium ,,Untersuchung nichtlinear-dynamischer Effekte in produktionstechnischen Systemen'' 1998, to appear.
B. Fiedler, D. Turaev
Normal forms, resonances, and meandering tip motions near relative equilibria of Euclidean group actions
Arch. Rational Mech. Analysis 145 (1998), 129-159.
(gziped postscript, 256 kB)     (pdf, 464 kB)
B. Fiedler, A. Scheel, M. I. Vishik
Large patterns of elliptic systems in infinite cylinders
J. Math. Pures Appl. 77 (1998), 879-907.
(gziped postscript, 108 kB)     (pdf, 320 kB)
B. Fiedler, S. Liebscher, J.C. Alexander
Generic Hopf bifurcation from lines of equilibria without parameters: I. Theory
J. Diff. Eq. 167 (2000), 16-35.
(gziped postscript, 238 kB)     (postscript, 2.0 MB)     (pdf, 2.6 MB)
B. Fiedler, S. Liebscher
Generic Hopf bifurcation from lines of equilibria without parameters: II. Systems of viscous hyperbolic balance laws
SIAM J. Math. Analysis 31 (2000), 1396-1404.
(gziped postscript, 209 kB)     (postscript, 1.9 MB)     (pdf, 2.5 MB)
B. Fiedler, S. Liebscher, J.C. Alexander
Generic Hopf bifurcation from lines of equilibria without parameters: III. Binary Oscillations
Int. J. Bif. Chaos 10 (2000), 1613-1622.
(gziped postscript, 210 kB)     (postscript, 1.9 MB)     (pdf, 2.5 MB)
M. Belhaq, B. Fiedler, F. Lakrad
Homoclinic connections in strongly self-excited nonlinear oscillators: the Melnikov function and the elliptic Lindstedt-Poincaré method
Nonlinear Dynamics 23 (2000), 67-86.
C. Rocha, B. Fiedler
Realization of meander permutations by boundary value problems
J. Diff. Eq. 156 (1999), 282-308.
(gziped postscript, 104 kB)     (pdf, 240 kB)
B. Fiedler, R.-M. Mantel
Crossover collisions of scroll wave filaments
Doc. Math. 5 (2000), 695-731.
(gziped postscript, 700 kB)     (pdf, 21696 kB)
B. Fiedler, M.I. Vishik
Quantitative homogenization of analytic semigroups and reaction-diffusion equations with Diophantine spatial frequencies
Advances in Differential Equations 6 (2001), 1377-1408.
(gziped postscript, 808 kB)     (pdf, 1092 kB)
B. Fiedler, M.I.Vishik
Quantitative homogenization of global attractors for reaction-diffusion systems with rapidly oscillating terms
Asympt. Analysis 34 (2003), 159-185.
(gziped postscript, 132 kB)     (pdf, 328 kB)
B. Fiedler, K. Gröger, J. Sprekels (eds.)
Equadiff 99, Proceedings of the International Conference on Differential Equations.
Berlin 1999, vol. I and II, World Scientific Publishers, Singapore 2000, 1487 p.
B. Fiedler (ed.)
Handbook of Dynamical Systems II.
Elsevier, Amsterdam, 2002, 1086 p.
B. Fiedler (ed.)
Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems.
Springer-Verlag, Heidelberg, 2001, 820 p.
B. Fiedler, S. Liebscher
Takens-Bogdanov bifurcations without parameters, and oscillatory shock profiles.
In H. Broer, B. Krauskopf, G. Vegter, editors, Global Analysis of Dynamical Systems, Festschrift dedicated to Floris Takens for his 60th birthday. IOP, Bristol, 2001, pp. 211-259.
(gziped postscript, 757 kB)     (pdf, 4550 kB)
B. Fiedler, C. Rocha, D. Salazar, J. Solà-Morales
Dynamics of piecewise-autonomous bistable parabolic equations.
In Differential Equations and Dynamical Systems, A. Galves, J.K. Hale, C. Rocha (eds.), Fields Institute Communications 31, 2002, 151-163.
(gziped postscript, 932 kB)     (pdf, 376 kB)
B. Fiedler, M. Vishik
Quantitative homogenization of global attractors of damped hyperbolic wave equations with spatially rapidly oscillating coefficients.
Russ. Math. Surv. 57 (2003), 709-728.
(postscript, 254 kB)     (pdf, 187 kB)
B. Fiedler, A. Scheel
Dynamics of Reaction-Diffusion Patterns.
In Trends in Nonlinear Analysis, Festschrift dedicated to Willi Jäger for his 60th birthday, M. Kirkilionis, R. Rannacher, F. Tomi (eds.), Springer-Verlag, Heidelberg, 2003, 23-152.
(gziped postscript, 9.4 MB)     (pdf, 3.3 MB)
B. Fiedler, C. Rocha, M. Wolfrum
Heteroclinic orbits between rotating waves of semilinear parabolic equations on the circle.
J. Differential Equations 201 (2004), 99-138.
Weierstrass-Institute preprint 832
B. Fiedler, S. Liebscher
Bifurcations without parameters: Some ODE and PDE examples.
T.-T. Li et al. (eds.), Proc. International Congress of Mathematicians, ICM 2002, Vol. III: Invited Lectures. Higher Education Press, Beijing, 305-316 (2002).
(gziped postscript, 2.2 MB)     (pdf, 2.9 MB)
B. Fiedler, J.-S. Guo, J.-C. Tsai
Multiplicity of rotating spirals under curvature flows with normal tip motion.
J. Differential Equations 205 (2004) 211-228.
(postscript, 360 kB)     (pdf, 180 kB)
B. Fiedler, J.-S. Guo, J.-C. Tsai
Rotating spirals of curvature flows: a center manifold approach.
Ann. Mat. Pura Appl. 135 (2006), 259-291.
(postscript, 4.2 MB)     (pdf, 1.4 MB)
A. Afendikov, B. Fiedler, S. Liebscher
Plane Kolmogorov fows and Takens-Bogdanov bifurcation without parameters: The doubly reversible case.
Asymptotic Analysis 60 (2008), pp. 135-211.
(pdf, 3.3 MB)
B. Fiedler, A. Schuppert
Local identification of hybrid models with tree structure
IMA J. Appl. Math 73 (2008), 449-476.
(postscript, 450 kB)     (pdf, 250 kB)
B. Fiedler, C. Rocha
Connectivity and Design of Planar Global Attractors of Sturm Type. I: Bipolar Orientations and Hamiltonian Paths
Crelle J. Reine Angew. Math. 635 (2009), 76-96.
(pdf, 750 kB)
B. Fiedler, C. Rocha
Connectivity and Design of Planar Global Attractors of Sturm Type. II: Connection Graphs.
J. Differential Equations 244 (2008), 1255-1286.
(pdf, 4.6 MB)
B. Fiedler, C. Rocha
Connectivity and Design of Planar Global Attractors of Sturm Type. III: Small and Platonic Examples.
J. Dyn. Diff. Equations 22 (2010), 121-162.
sections 1&2 (pdf, 2.4 MB), section 3 (pdf, 5.6 MB), section 4 (pdf, 5.7 MB).
B. Fiedler, H. Matano
Global dynamics of blow-up profiles in one-dimensional reaction diffusion equations
J. Dyn. Diff. Equations 19 (2007), 867-893.
(pdf, 250 kB)
B. Fiedler, S.-B. Hsu
Non-periodicity in chemostat equations: a multi-dimensional negative Bendixson-Dulac criterion
J. Math. Biology 59 (2008), 233-253.
(pdf, 310 kB)
L. Schimansky-Geier, B. Fiedler, J. Kurths, E. Schöll (eds.)
Analysis and Control of Complex Nonlinear Processes in Physics, Chemistry and Biology.
Dedicated to Werner Ebeling and Gerhard Ertl.
Lect. Notes in Complex Systems 5, World Scientific, Singapore 2007, 452 pp.
B. Fiedler
Roots and centralizers of Anosov diffeomorphisms on tori.
Int. J. Bifurcation Chaos 15 (2005), 3691-3699.
(pdf, 201 kB)
A.L. Afendikov, S. Liebscher, B. Fiedler
Standing waves near the Kolmogorov flow.
Dokl. Math. 75 (2007), 283-286,
translation from Dokl. Akad. Nauk 413 (2007), 587-590.
B. Fiedler, V. Flunkert, M. Georgi, P. Hövel, E. Schöll
Refuting the odd number limitation of time-delayed feedback control.
Phys. Rev. Lett. 98 (2007), 114101.
(pdf, 605 kB)
W. Just, B. Fiedler, V. Flunkert, M. Georgi, P. Hövel, E. Schöll
Beyond the odd number limitation: A bifurcation analysis of time-delayed feedback control.
Phys. Rev. E 76 (2007), 026210.
(pdf, 473 kB)
B. Fiedler, M. Georgi, N. Jangle
Spiral wave dynamics: reaction and diffusion versus kinematics.
In Analysis and Control of Complex Nonlinear Processes in Physics, Chemistry and Biology, L. Schimansky-Geier (ed.) et al.,
Lect. Notes in Complex Systems 5, World Scientific, Singapore 2007, 69-114.
(pdf, 1.1 MB)
B. Fiedler, V. Flunkert, M. Georgi, P. Hövel, E. Schöll
Beyond the odd-number limitation of time-delayed feedback control.
In Handbook of Chaos Control, E. Schöll (ed.) et al.
Wiley-VCH, Weinheim 2008, 73-84.
(pdf, 519 kB)     (handbook)
B. Fiedler, V. Flunkert, M. Georgi, P. Hövel, E. Schöll
Delay stabilization of rotating waves without odd number limitation.
In Reviews of Nonlinear Dynamics and Complexity 1, H.G. Schuster (ed.),
Wiley-VCH, Weinheim 2008, 53-67.
(pdf, 425 kB)
B. Fiedler, S. Yanchuk, V. Flunkert, P. Hövel, H.-J. Wünsche, E. Schöll
Delay stabilization of rotating waves near fold bifurcation and application to all-optical control of a semiconductor laser.
Phys. Rev. E 77 (2008), 066207.
(pdf, 765 kB)
B. Fiedler
Time-delayed feedback control: qualitative promise and quantitative constraint.
In A.L. Fradkov et al. (eds.), 6th EUROMECH Conference on Nonlinear Dynamics ENOC 2008,
Saint Petersburg, Russia, 2008.
(pdf, 133 kB)     (lib.physcon.ru).
B. Fiedler, V. Flunkert, P. Hövel, E. Schöll
Delay stabilization of periodic orbits in coupled oscillator systems.
Phil. Trans. Roy. Soc. A 368 (2010), 319-341.
(pdf, 512 kB)
B. Fiedler
Romeo and Juliet, Spontaneous Pattern Formation, and Turing's Instability.
In Mathematics Everywhere, M. Aigner et al. (eds.),
AMS, Providence 2010, 57-75.
(pdf, 946kB)
A. Afendikov, B. Fiedler, S. Liebscher
Plane Kolmogorov flows and Takens-Bogdanov bifurcation without parameters. The singly reversible case.
Asymptotic Analysis 72 (2011), pp. 31-76.
(journal)
B. Fiedler, C. Rocha, M. Wolfrum
Sturm global attractors for S1-equivariant parabolic equations.
Netw. Heterog. Media 7 (2012), 617-659.
(pdf, 487 kB)
B. Fiedler, C. Rocha, M. Wolfrum
A permutation characterization of Sturm global attractors of Hamiltonian type.
J. Differ. Equations 252 (2012), 588-623.
(pdf, 414 kB)
B. Fiedler, C. Grotta-Ragazzo, C. Rocha
An explicit Lyapunov function for reflection symmetric parabolic partial differential equations on the circle.
Russian Math. Surveys (2012), to appear.
(pdf, 184 kB)
B. Fiedler
Mathematical models of flageolet harmonics on stringed instruments.
J. Comp. Appl. Math. 254 (2013), 144-153.
(pdf, 300 kB)
B. Fiedler, C. Rocha
Schoenflies spheres as boundaries of bounded unstable manifolds in gradient Sturm systems.
J. Dyn. Diff. Equat. (2013), to appear.
(pdf, 433 kB)
B. Fiedler, P. Castaneda
Rainbow meanders and Cartesian billiards.
São Paulo J. Math. Sci. 6 (2012), 247-275.
(pdf, 859 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)
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)
B. Fiedler
Reversibility, continued fractions, and infinite meander permutations of planar homoclinic orbits in linear hyperbolic Anosov maps.
Int. J. Bifurcation Chaos Appl. Sci. Eng. (2014), to appear.
(pdf, 269 kB)
B. Fiedler, C. Rocha
Nonlinear Sturm global attractors: unstable manifold decompositions as CW-complexes.
Submitted 2014.
(pdf, 512 kB)
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