Prof. Dr. Bernold Fiedler

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.

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.
Weierstrass-Institute preprint 832, 2003.

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

Existence of steadily rotating spiral waves.
In preparation 2003.
(postscript, 360 kB)     (pdf, 180 kB)

B. Fiedler, J.-S. Guo, J.-C. Tsai

Rotating spirals of curvature flows: a center manifold approach.
In preparation 2003.
(postscript, 4.2 MB)     (pdf, 1.4 MB)

A. Afendikov, B. Fiedler, S. Liebscher

Standing waves of plane Kolmogorov flows, and symmetric Takens-Bogdanov bifurcation without parameters
In preparation, 2004.

B. Fiedler, A. Schuppert

Local identification of scalar hybrid models with tree structure
In preparation, 2004.
(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
Submitted, 2007.
(pdf, 750 kB)

B. Fiedler, C. Rocha

Connectivity and Design of Planar Global Attractors of Sturm Type. II: Connection Graphs.
Submitted, 2007.
(pdf, 4.6 MB)

B. Fiedler, C. Rocha

Connectivity and Design of Planar Global Attractors of Sturm Type. III: Small and Platonic Examples.
Submitted, 2007.
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. Eqs., in press 2007.
(pdf, 250 kB)

B. Fiedler, S.-B. Hsu

Non-periodicity in chemostat equations: a multi-dimensional negative Bendixson-Dulac criterion
J. Math. Biology, in press 2008.
(pdf, 310 kB)