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## Fiedler, Bernold

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 Author ID: fiedler.bernold Published as: Fiedler, Bernold; Fiedler, B. Homepage: http://dynamics.mi.fu-berlin.de/persons/fiedler.php External Links: MGP · Wikidata · GND · IdRef · theses.fr
 Documents Indexed: 105 Publications since 1983, including 8 Books Biographic References: 1 Publication
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#### Co-Authors

 16 single-authored 15 Rocha, Carlos 8 Liebscher, Stefan 6 Brunovský, Pavol 4 Mochizuki, Atsushi 4 Sandstede, Björn 4 Schuppert, Andreas A. 4 Vishik, Marko Iosifovich 3 Afendikov, Andrei L. 3 Alexander, James Crew 3 Efendiev, Messoud 3 Flunkert, Valentin 3 Georgi, Marc 3 Hövel, Philipp 3 Scheel, Arnd 3 Schöll, Eckehard 3 Wolfrum, Matthias 2 Belhaq, Mohamed 2 Beyn, Wolf-Jürgen 2 Gedeon, Tomáš 2 Gröger, Konrad 2 Guo, Jong-Shenq 2 Heinze, Steffen 2 Hsu, Szebi 2 Kunkel, Peter 2 Kurosawa, Gen 2 Mallet-Paret, John Joseph 2 Saito, Daisuke 2 Schneider, Isabelle 2 Sprekels, Jürgen 2 Tsai, Je-Chiang 2 Turaev, Dmitry V. 1 Angenent, Sigurd Bernardus 1 Behrends, Ehrhard 1 Brehm, Bernhard 1 Castañeda, Pablo 1 Dangelmayr, Gerhard 1 de Wolff, Babette 1 Deng, Bo 1 Deuflhard, Peter 1 Haugland, Sindre W. 1 Hell, Juliette 1 Houssni, Mohamed 1 Jangle, Nihar 1 Kemeth, Felix P. 1 Kirchgässner, Klaus 1 Krischer, Katharina 1 Kurths, Jürgen 1 Lakrad, Faouzi 1 Lappicy, Phillipo 1 Lin, Hsiu-Hau 1 Mantel, Rolf-Martin 1 Matano, Hiroshi 1 Mielke, Alexander 1 Mischaikow, Konstantin 1 Muniz Oliva, Sergio Muniz 1 Nieto, Alejandro López 1 Poláčik, Peter 1 Rademacher, Jens Diederich Michael 1 Rand, Richard H. 1 Sah, Si Mohamed 1 Salazar, Domingo 1 Scheurle, Jürgen 1 Schimansky-Geier, Lutz 1 Solà-Morales, Joan 1 Vanderbauwhede, Andre L. 1 Wulff, Claudia
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#### Serials

 12 Journal of Differential Equations 7 Journal of Dynamics and Differential Equations 4 Archive for Rational Mechanics and Analysis 4 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 3 Journal für die Reine und Angewandte Mathematik 3 Asymptotic Analysis 3 SIAM Journal on Mathematical Analysis 3 Documenta Mathematica 3 São Paulo Journal of Mathematical Sciences 2 Mathematical Methods in the Applied Sciences 2 Russian Mathematical Surveys 2 ZAMP. Zeitschrift für angewandte Mathematik und Physik 2 Transactions of the American Mathematical Society 2 Ergodic Theory and Dynamical Systems 2 Discrete and Continuous Dynamical Systems 2 Oberwolfach Reports 2 Discrete and Continuous Dynamical Systems. Series S 2 Journal of Theoretical Biology 1 IMA Journal of Applied Mathematics 1 Journal of Mathematical Biology 1 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Journal of Computational and Applied Mathematics 1 Memoirs of the American Mathematical Society 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Physica D 1 RAIRO. Modélisation Mathématique et Analyse Numérique 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Tatra Mountains Mathematical Publications 1 Advances in Differential Equations 1 Doklady Mathematics 1 Nonlinear Dynamics 1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Discrete and Continuous Dynamical Systems. Series B 1 SIAM Journal on Applied Dynamical Systems 1 Lecture Notes in Mathematics 1 World Scientific Lecture Notes in Complex Systems 1 Networks and Heterogeneous Media 1 Nonlinear Analysis. Theory, Methods & Applications
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#### Fields

 58 Partial differential equations (35-XX) 56 Dynamical systems and ergodic theory (37-XX) 37 Ordinary differential equations (34-XX) 14 Biology and other natural sciences (92-XX) 9 General and overarching topics; collections (00-XX) 8 Numerical analysis (65-XX) 7 Combinatorics (05-XX) 6 Classical thermodynamics, heat transfer (80-XX) 5 Fluid mechanics (76-XX) 5 Systems theory; control (93-XX) 4 Operator theory (47-XX) 4 Mechanics of particles and systems (70-XX) 3 Manifolds and cell complexes (57-XX) 3 Global analysis, analysis on manifolds (58-XX) 3 Statistical mechanics, structure of matter (82-XX) 2 Integral equations (45-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Algebraic topology (55-XX) 1 Computer science (68-XX) 1 Mechanics of deformable solids (74-XX) 1 Quantum theory (81-XX) 1 Relativity and gravitational theory (83-XX) 1 Operations research, mathematical programming (90-XX) 1 Information and communication theory, circuits (94-XX)

#### Citations contained in zbMATH Open

88 Publications have been cited 1,007 times in 596 Documents Cited by Year
Homoclinic bifurcation at resonant eigenvalues. Zbl 0703.34050
Chow, Shui-Nee; Deng, Bo; Fiedler, Bernold
1990
Heteroclinic orbits of semilinear parabolic equations. Zbl 0849.35056
Fiedler, Bernold; Rocha, Carlos
1996
Homoclinic period blow-up in reversible and conservative systems. Zbl 0762.34023
Vanderbauwhede, André; Fiedler, Bernold
1992
Connecting orbits in scalar reaction diffusion equations. II: The complete solution. Zbl 0699.35144
Brunovský, P.; Fiedler, B.
1989
A Poincaré-Bendixson theorem for scalar reaction diffusion equations. Zbl 0704.35070
Fiedler, Bernold; Mallet-Paret, John
1989
Global bifurcation of periodic solutions with symmetry. Zbl 0644.34038
Fiedler, Bernold
1988
The dynamics of rotating waves in scalar reaction diffusion equations. Zbl 0696.35086
Angenent, S. B.; Fiedler, B.
1988
Connecting orbits in scalar reaction diffusion equations. Zbl 0679.35047
Brunovský, P.; Fiedler, B.
1988
Orbit equivalence of global attractors of semilinear parabolic differential equations. Zbl 0932.37065
Fiedler, Bernold; Rocha, Carlos
2000
Complicated dynamics of scalar reaction diffusion equations with a nonlocal term. Zbl 0726.35060
Fiedler, Bernold; Poláčik, Peter
1990
Numbers of zeros on invariant manifolds in reaction-diffusion equations. Zbl 0594.35056
Brunovský, Pavol; Fiedler, Bernold
1986
Spatio-temporal dynamics of reaction-diffusion patterns. Zbl 1082.37004
Fiedler, Bernold; Scheel, Arnd
2003
Homoclinic connections in strongly self-excited nonlinear oscillators: The Melnikov function and the elliptic Lindstedt-Poincaré method. Zbl 0967.70019
Belhaq, Mohamed; Fiedler, Bernold; Lakrad, Faouzi
2000
Bifurcation from relative equilibria of noncompact group actions: Skew products, meanders, and drifts. Zbl 0870.58014
Fiedler, Bernold; Sandstede, Björn; Scheel, Arnd; Wulff, Claudia
1996
Discretization of homoclinic orbits, rapid forcing and “invisible” chaos. Zbl 0923.34049
Fiedler, Bernold; Scheurle, Jürgen
1996
Realization of meander permutations by boundary value problems. Zbl 0935.34018
Fiedler, Bernold; Rocha, Carlos
1999
Heteroclinic orbits between rotating waves of semilinear parabolic equations on the circle. Zbl 1064.35076
Fiedler, Bernold; Rocha, Carlos; Wolfrum, Matthias
2004
Generic Hopf bifurcation from lines of equilibria without parameters. I: Theory. Zbl 0978.34035
Fiedler, Bernold; Liebscher, Stefan; Alexander, J. C.
2000
Dynamics of periodically forced parabolic equations on the circle. Zbl 0754.35066
Sandstede, Björn; Fiedler, Bernold
1992
Delay stabilization of periodic orbits in coupled oscillator systems. Zbl 1201.34103
Fiedler, B.; Flunkert, V.; Hövel, P.; Schöll, E.
2010
Connections between Morse sets for delay-differential equations. Zbl 0659.34077
Fiedler, Bernold; Maller-Paret, John
1989
Generic Hopf bifurcation from lines of equilibria without parameters. III. Binary oscillations. Zbl 1090.37556
Fiedler, Bernold; Liebscher, Stefan; Alexander, J. C.
2000
Quantitative homogenization of global attractors for reaction-diffusion systems with rapidly oscillating terms. Zbl 1135.35315
Fiedler, Bernold; Vishik, Mark I.
2003
An index for global Hopf bifurcation in parabolic systems. Zbl 0554.35010
Fiedler, Bernold
1985
Dynamics of nonlinear waves in dissipative systems: reduction, bifurcation and stability. Zbl 0866.35002
Dangelmayr, Gerhard; Fiedler, Bernold; Kirchgässner, Klaus; Mielke, Alexander
1996
Basins of attraction in strongly damped coupled mechanical oscillators: A global example. Zbl 0919.70012
Fiedler, Bernold; Belhaq, Mohamed; Houssni, Mohamed
1999
Global attractors of one-dimensional parabolic equations: Sixteen examples. Zbl 0814.35056
Fiedler, Bernold
1994
Dynamics and control at feedback vertex sets. I: Informative and determining nodes in regulatory networks. Zbl 1337.92074
Fiedler, Bernold; Mochizuki, Atsushi; Kurosawa, Gen; Saito, Daisuke
2013
Generic Hopf bifurcation from lines of equilibria without parameters: II. Systems of viscous hyperbolic balance laws. Zbl 0980.35098
Fiedler, Bernold; Liebscher, Stefan
2000
Dynamics of bifurcations for variational problems with $$O(3)$$ equivariance: A Conley index approach. Zbl 0756.49003
Fiedler, Bernold; Mischaikow, Konstantin
1992
Global Hopf bifurcation of two-parameter flows. Zbl 0603.58015
Fiedler, Bernold
1986
Quantitative homogenization of analytic semigroups and reaction-diffusion equations with Diophantine spatial frequencies. Zbl 1036.35022
Fiedler, Bernold; Vishik, Mark I.
2001
Connectivity and design of planar global attractors of Sturm type. I: Bipolar orientations and Hamiltonian paths. Zbl 1201.37102
Fiedler, Bernold; Rocha, Carlos
2009
Connectivity and design of planar global attractors of Sturm type. II: Connection graphs. Zbl 1179.35069
Fiedler, Bernold; Rocha, Carlos
2008
Do global attractors depend on boundary conditions? Zbl 0855.58053
Fiedler, Bernold
1996
Coalescence of reversible homoclinic orbits causes elliptic resonance. Zbl 0876.34057
Fiedler, Bernold; Turaev, Dimitry
1996
Multiplicity of rotating spirals under curvature flows with normal tip motion. Zbl 1063.34001
Fiedler, Bernold; Guo, Jong-Shenq; Tsai, Je-Chiang
2004
A class of convergent neural network dynamics. Zbl 0944.34039
Fiedler, Bernold; Gedeon, Tomáš
1998
Large patterns of elliptic systems in infinite cylinders. Zbl 0917.35011
Fiedler, Bernold; Scheel, Arnd; Vishik, Mark I.
1998
Normal forms, resonances, and meandering tip motions near relative equilibria of Euclidean group actions. Zbl 0957.37026
Fiedler, Bernold; Turaev, Dmitry
1998
Connectivity and design of planar global attractors of Sturm type. III: Small and platonic examples. Zbl 1204.35106
Fiedler, Bernold; Rocha, Carlos
2010
Dynamics and control at feedback vertex sets. II: A faithful monitor to determine the diversity of molecular activities in regulatory networks. Zbl 1397.92256
Mochizuki, Atsushi; Fiedler, Bernold; Kurosawa, Gen; Saito, Daisuke
2013
Quantitative homogenization of global attractors for hyperbolic wave equations with rapidly oscillating coefficients. Zbl 1055.35025
Fiedler, B.; Vishik, M. I.
2002
An explicit Lyapunov function for reflection symmetric parabolic partial differential equations on the circle. Zbl 1307.35058
Fiedler, B.; Grotta-Ragazzo, C.; Rocha, C.
2014
A Lyapunov function for tridiagonal competitive-cooperative systems. Zbl 0922.34041
Fiedler, Bernold; Gedeon, Tomás
1999
Delayed feedback control of a delay equation at Hopf bifurcation. Zbl 1358.34079
Fiedler, Bernold; Muniz Oliva, Sergio Muniz
2016
Rotating spirals of curvature flows: a center manifold approach. Zbl 1223.37110
Fiedler, Bernold; Guo, Jong-Shenq; Tsai, Je-Chiang
2006
Beyond the odd-number limitation of time-delayed feedback control. 2nd completely revised and enlarged ed. Zbl 1183.93062
Fiedler, Bernold; Flunkert, Valentin; Goergi, Marc; Hövel, Philipp
2008
Schoenflies spheres as boundaries of bounded unstable manifolds in gradient Sturm systems. Zbl 1375.35259
Fiedler, Bernold; Rocha, Carlos
2015
Discrete Lyapunov functionals and $$\omega$$-limit sets. Zbl 0688.58041
Fiedler, Bernold
1989
Simplicity of zeros in scalar parabolic equations. Zbl 0549.35062
Brunovský, P.; Fiedler, B.
1986
Handbook of dynamical systems. Volume 2. Zbl 0982.37002
Fiedler, Bernold (ed.)
2002
Global pathfollowing of homoclinic orbits in twoparameter flows. Zbl 0866.35004
Fiedler, B.
1996
Non-periodicity in chemostat equations: a multi-dimensional negative Bendixson-Dulac criterion. Zbl 1231.92061
Fiedler, Bernold; Hsu, Sze-Bi
2009
Global Hopf bifurcation in porous catalysts. Zbl 0528.35007
Fiedler, Bernold
1983
A permutation characterization of Sturm global attractors of Hamiltonian type. Zbl 1233.35042
Fiedler, Bernold; Rocha, Carlos; Wolfrum, Matthias
2012
Nonlinear Sturm global attractors: unstable manifold decompositions as regular CW-complexes. Zbl 1327.35194
Fiedler, Bernold; Rocha, Carlos
2014
Periods of discretized linear Anosov maps. Zbl 0915.58075
Behrends, Ehrhard; Fiedler, Bernold
1998
Delay stabilization of rotating waves without odd number limitation. Zbl 1160.37429
Fiedler, Bernold; Flunkert, Valentin; Georgi, Marc; Hövel, Philipp; Schöll, Eckehard
2008
Sturm 3-ball global attractors 3: examples of Thom-Smale complexes. Zbl 1396.37036
Fiedler, Bernold; Rocha, Carlos
2018
Sturm global attractors for $$S^1$$-equivariant parabolic equations. Zbl 1262.35053
Fiedler, Bernold; Rocha, Carlos; Wolfrum, Matthias
2012
Sensitivity of chemical reaction networks: A structural approach. 3. regular multimolecular systems. Zbl 1388.82017
Brehm, Bernhard; Fiedler, Bernold
2018
Rainbow meanders and Cartesian billiards. Zbl 1333.37015
Fiedler, Bernold; Castañeda, Pablo
2012
Sensitivity of chemical reaction networks: a structural approach. 2. Regular monomolecular systems. Zbl 1333.94079
Fiedler, Bernold; Mochizuki, Atsushi
2015
Homotopy invariants of time reversible periodic orbits. I: Theory. Zbl 0852.34038
Fiedler, Bernold; Heinze, Steffen
1996
Roots and centralizers of Anosov diffeomorphisms on tori. Zbl 1097.37015
Fiedler, Bernold
2005
Connections in scalar reaction diffusion equations with Neumann boundary condition. Zbl 0616.35044
Fiedler, B.; Brunovský, P.
1986
Global Hopf bifurcation for Volterra integral equations. Zbl 0605.45002
Fiedler, Bernold
1986
Sensitivity of chemical reaction networks: a structural approach. 1. Examples and the carbon metabolic network. Zbl 1412.92098
Mochizuki, Atsushi; Fiedler, Bernold
2015
Analysis and control of complex nonlinear processes in physics, chemistry and biology. Zbl 1110.82004
Schimansky-Geier, L. (ed.); Fiedler, B. (ed.); Kurths, J. (ed.); Schöll, E. (ed.)
2007
Takens-Bogdanov bifurcations without parameters and oscillatory shock profiles. Zbl 1198.37082
Fiedler, Bernold; Liebscher, Stefan
2001
Bifurcations without parameters: Some ODE and PDE examples. Zbl 1037.34033
Fiedler, Bernold; Liebscher, Stefan
2002
Dynamics of piecewise-autonomous bistable parabolic equations. Zbl 1004.35069
Fiedler, Bernold; Rocha, Carlos; Salazar, Domingo; Solà-Morales, Joan
2002
Thermically stable upscaling of an exothermic model reaction. (Thermisch stabiles Upscaling einer exothermen Modellreaktion.) Zbl 0867.76091
Fiedler, B.; Efendiev, M.; Schuppert, A.
1997
Plane Kolmogorov flows and Takens-Bogdanov bifurcation without parameters: the singly reversible case. Zbl 1233.37054
Afendikov, Andrei; Fiedler, Bernold; Liebscher, Stefan
2011
Global decoupling of coupled symmetric oscillators. Zbl 0678.34038
Alexander, J. C.; Fiedler, B.
1989
Upscaling of some exothermic reactions from chemical industry. Zbl 0887.92033
Efendiev, M. A.; Fiedler, B.; Schuppert, A.
1996
Homotopy invariants of time reversible periodic orbits. II: Towards applications. Zbl 0852.34039
Fiedler, Bernold; Heinze, Steffen
1996
Anisotropic Einstein data with isotropic non negative prescribed scalar curvature. Zbl 1332.35358
Fiedler, Bernold; Hell, Juliette; Smith, Brian
2015
Numerical pathfollowing beyond critical points in ODE models. Zbl 0617.65094
Deuflhard, P.; Fiedler, B.; Kunkel, P.
1987
Heteroclinic connections of stationary solutions of scalar reaction- diffusion equations. Zbl 0661.35050
Brunovský, P.; Fiedler, B.
1987
Local identification of scalar hybrid models with tree structure. Zbl 1211.93040
Fiedler, Bernold; Schuppert, Andreas
2008
Global dynamics of blow-up profiles in one-dimensional reaction diffusion equations. Zbl 1132.35048
Fiedler, Bernold; Matano, Hiroshi
2007
Sturm 3-ball global attractors. 1: Thom-Smale complexes and meanders. Zbl 1408.37027
Fiedler, Bernold; Rocha, Carlos
2018
A Lyapunov function for fully nonlinear parabolic equations in one spatial variable. Zbl 1415.35155
Lappicy, Phillipo; Fiedler, Bernold
2019
Sturm 3-ball global attractors 2: design of Thom-Smale complexes. Zbl 1423.35040
Fiedler, Bernold; Rocha, Carlos
2019
Coexistence of infinitely many large, stable, rapidly oscillating periodic solutions in time-delayed Duffing oscillators. Zbl 1443.34070
Fiedler, Bernold; Nieto, Alejandro López; Rand, Richard H.; Sah, Si Mohamed; Schneider, Isabelle; de Wolff, Babette
2020
Global Hopf bifurcation in networks with fast feedback cycles. Zbl 1454.34060
Fiedler, Bernold
2021
Global Hopf bifurcation in networks with fast feedback cycles. Zbl 1454.34060
Fiedler, Bernold
2021
Coexistence of infinitely many large, stable, rapidly oscillating periodic solutions in time-delayed Duffing oscillators. Zbl 1443.34070
Fiedler, Bernold; Nieto, Alejandro López; Rand, Richard H.; Sah, Si Mohamed; Schneider, Isabelle; de Wolff, Babette
2020
A Lyapunov function for fully nonlinear parabolic equations in one spatial variable. Zbl 1415.35155
Lappicy, Phillipo; Fiedler, Bernold
2019
Sturm 3-ball global attractors 2: design of Thom-Smale complexes. Zbl 1423.35040
Fiedler, Bernold; Rocha, Carlos
2019
Sturm 3-ball global attractors 3: examples of Thom-Smale complexes. Zbl 1396.37036
Fiedler, Bernold; Rocha, Carlos
2018
Sensitivity of chemical reaction networks: A structural approach. 3. regular multimolecular systems. Zbl 1388.82017
Brehm, Bernhard; Fiedler, Bernold
2018
Sturm 3-ball global attractors. 1: Thom-Smale complexes and meanders. Zbl 1408.37027
Fiedler, Bernold; Rocha, Carlos
2018
Delayed feedback control of a delay equation at Hopf bifurcation. Zbl 1358.34079
Fiedler, Bernold; Muniz Oliva, Sergio Muniz
2016
Schoenflies spheres as boundaries of bounded unstable manifolds in gradient Sturm systems. Zbl 1375.35259
Fiedler, Bernold; Rocha, Carlos
2015
Sensitivity of chemical reaction networks: a structural approach. 2. Regular monomolecular systems. Zbl 1333.94079
Fiedler, Bernold; Mochizuki, Atsushi
2015
Sensitivity of chemical reaction networks: a structural approach. 1. Examples and the carbon metabolic network. Zbl 1412.92098
Mochizuki, Atsushi; Fiedler, Bernold
2015
Anisotropic Einstein data with isotropic non negative prescribed scalar curvature. Zbl 1332.35358
Fiedler, Bernold; Hell, Juliette; Smith, Brian
2015
An explicit Lyapunov function for reflection symmetric parabolic partial differential equations on the circle. Zbl 1307.35058
Fiedler, B.; Grotta-Ragazzo, C.; Rocha, C.
2014
Nonlinear Sturm global attractors: unstable manifold decompositions as regular CW-complexes. Zbl 1327.35194
Fiedler, Bernold; Rocha, Carlos
2014
Dynamics and control at feedback vertex sets. I: Informative and determining nodes in regulatory networks. Zbl 1337.92074
Fiedler, Bernold; Mochizuki, Atsushi; Kurosawa, Gen; Saito, Daisuke
2013
Dynamics and control at feedback vertex sets. II: A faithful monitor to determine the diversity of molecular activities in regulatory networks. Zbl 1397.92256
Mochizuki, Atsushi; Fiedler, Bernold; Kurosawa, Gen; Saito, Daisuke
2013
A permutation characterization of Sturm global attractors of Hamiltonian type. Zbl 1233.35042
Fiedler, Bernold; Rocha, Carlos; Wolfrum, Matthias
2012
Sturm global attractors for $$S^1$$-equivariant parabolic equations. Zbl 1262.35053
Fiedler, Bernold; Rocha, Carlos; Wolfrum, Matthias
2012
Rainbow meanders and Cartesian billiards. Zbl 1333.37015
Fiedler, Bernold; Castañeda, Pablo
2012
Plane Kolmogorov flows and Takens-Bogdanov bifurcation without parameters: the singly reversible case. Zbl 1233.37054
Afendikov, Andrei; Fiedler, Bernold; Liebscher, Stefan
2011
Delay stabilization of periodic orbits in coupled oscillator systems. Zbl 1201.34103
Fiedler, B.; Flunkert, V.; Hövel, P.; Schöll, E.
2010
Connectivity and design of planar global attractors of Sturm type. III: Small and platonic examples. Zbl 1204.35106
Fiedler, Bernold; Rocha, Carlos
2010
Connectivity and design of planar global attractors of Sturm type. I: Bipolar orientations and Hamiltonian paths. Zbl 1201.37102
Fiedler, Bernold; Rocha, Carlos
2009
Non-periodicity in chemostat equations: a multi-dimensional negative Bendixson-Dulac criterion. Zbl 1231.92061
Fiedler, Bernold; Hsu, Sze-Bi
2009
Connectivity and design of planar global attractors of Sturm type. II: Connection graphs. Zbl 1179.35069
Fiedler, Bernold; Rocha, Carlos
2008
Beyond the odd-number limitation of time-delayed feedback control. 2nd completely revised and enlarged ed. Zbl 1183.93062
Fiedler, Bernold; Flunkert, Valentin; Goergi, Marc; Hövel, Philipp
2008
Delay stabilization of rotating waves without odd number limitation. Zbl 1160.37429
Fiedler, Bernold; Flunkert, Valentin; Georgi, Marc; Hövel, Philipp; Schöll, Eckehard
2008
Local identification of scalar hybrid models with tree structure. Zbl 1211.93040
Fiedler, Bernold; Schuppert, Andreas
2008
Analysis and control of complex nonlinear processes in physics, chemistry and biology. Zbl 1110.82004
Schimansky-Geier, L.; Fiedler, B.; Kurths, J.; Schöll, E.
2007
Global dynamics of blow-up profiles in one-dimensional reaction diffusion equations. Zbl 1132.35048
Fiedler, Bernold; Matano, Hiroshi
2007
Rotating spirals of curvature flows: a center manifold approach. Zbl 1223.37110
Fiedler, Bernold; Guo, Jong-Shenq; Tsai, Je-Chiang
2006
Roots and centralizers of Anosov diffeomorphisms on tori. Zbl 1097.37015
Fiedler, Bernold
2005
Heteroclinic orbits between rotating waves of semilinear parabolic equations on the circle. Zbl 1064.35076
Fiedler, Bernold; Rocha, Carlos; Wolfrum, Matthias
2004
Multiplicity of rotating spirals under curvature flows with normal tip motion. Zbl 1063.34001
Fiedler, Bernold; Guo, Jong-Shenq; Tsai, Je-Chiang
2004
Spatio-temporal dynamics of reaction-diffusion patterns. Zbl 1082.37004
Fiedler, Bernold; Scheel, Arnd
2003
Quantitative homogenization of global attractors for reaction-diffusion systems with rapidly oscillating terms. Zbl 1135.35315
Fiedler, Bernold; Vishik, Mark I.
2003
Quantitative homogenization of global attractors for hyperbolic wave equations with rapidly oscillating coefficients. Zbl 1055.35025
Fiedler, B.; Vishik, M. I.
2002
Handbook of dynamical systems. Volume 2. Zbl 0982.37002
Fiedler, Bernold
2002
Bifurcations without parameters: Some ODE and PDE examples. Zbl 1037.34033
Fiedler, Bernold; Liebscher, Stefan
2002
Dynamics of piecewise-autonomous bistable parabolic equations. Zbl 1004.35069
Fiedler, Bernold; Rocha, Carlos; Salazar, Domingo; Solà-Morales, Joan
2002
Quantitative homogenization of analytic semigroups and reaction-diffusion equations with Diophantine spatial frequencies. Zbl 1036.35022
Fiedler, Bernold; Vishik, Mark I.
2001
Takens-Bogdanov bifurcations without parameters and oscillatory shock profiles. Zbl 1198.37082
Fiedler, Bernold; Liebscher, Stefan
2001
Orbit equivalence of global attractors of semilinear parabolic differential equations. Zbl 0932.37065
Fiedler, Bernold; Rocha, Carlos
2000
Homoclinic connections in strongly self-excited nonlinear oscillators: The Melnikov function and the elliptic Lindstedt-Poincaré method. Zbl 0967.70019
Belhaq, Mohamed; Fiedler, Bernold; Lakrad, Faouzi
2000
Generic Hopf bifurcation from lines of equilibria without parameters. I: Theory. Zbl 0978.34035
Fiedler, Bernold; Liebscher, Stefan; Alexander, J. C.
2000
Generic Hopf bifurcation from lines of equilibria without parameters. III. Binary oscillations. Zbl 1090.37556
Fiedler, Bernold; Liebscher, Stefan; Alexander, J. C.
2000
Generic Hopf bifurcation from lines of equilibria without parameters: II. Systems of viscous hyperbolic balance laws. Zbl 0980.35098
Fiedler, Bernold; Liebscher, Stefan
2000
Realization of meander permutations by boundary value problems. Zbl 0935.34018
Fiedler, Bernold; Rocha, Carlos
1999
Basins of attraction in strongly damped coupled mechanical oscillators: A global example. Zbl 0919.70012
Fiedler, Bernold; Belhaq, Mohamed; Houssni, Mohamed
1999
A Lyapunov function for tridiagonal competitive-cooperative systems. Zbl 0922.34041
Fiedler, Bernold; Gedeon, Tomás
1999
A class of convergent neural network dynamics. Zbl 0944.34039
Fiedler, Bernold; Gedeon, Tomáš
1998
Large patterns of elliptic systems in infinite cylinders. Zbl 0917.35011
Fiedler, Bernold; Scheel, Arnd; Vishik, Mark I.
1998
Normal forms, resonances, and meandering tip motions near relative equilibria of Euclidean group actions. Zbl 0957.37026
Fiedler, Bernold; Turaev, Dmitry
1998
Periods of discretized linear Anosov maps. Zbl 0915.58075
Behrends, Ehrhard; Fiedler, Bernold
1998
Thermically stable upscaling of an exothermic model reaction. (Thermisch stabiles Upscaling einer exothermen Modellreaktion.) Zbl 0867.76091
Fiedler, B.; Efendiev, M.; Schuppert, A.
1997
Heteroclinic orbits of semilinear parabolic equations. Zbl 0849.35056
Fiedler, Bernold; Rocha, Carlos
1996
Bifurcation from relative equilibria of noncompact group actions: Skew products, meanders, and drifts. Zbl 0870.58014
Fiedler, Bernold; Sandstede, Björn; Scheel, Arnd; Wulff, Claudia
1996
Discretization of homoclinic orbits, rapid forcing and “invisible” chaos. Zbl 0923.34049
Fiedler, Bernold; Scheurle, Jürgen
1996
Dynamics of nonlinear waves in dissipative systems: reduction, bifurcation and stability. Zbl 0866.35002
Dangelmayr, Gerhard; Fiedler, Bernold; Kirchgässner, Klaus; Mielke, Alexander
1996
Do global attractors depend on boundary conditions? Zbl 0855.58053
Fiedler, Bernold
1996
Coalescence of reversible homoclinic orbits causes elliptic resonance. Zbl 0876.34057
Fiedler, Bernold; Turaev, Dimitry
1996
Global pathfollowing of homoclinic orbits in twoparameter flows. Zbl 0866.35004
Fiedler, B.
1996
Homotopy invariants of time reversible periodic orbits. I: Theory. Zbl 0852.34038
Fiedler, Bernold; Heinze, Steffen
1996
Upscaling of some exothermic reactions from chemical industry. Zbl 0887.92033
Efendiev, M. A.; Fiedler, B.; Schuppert, A.
1996
Homotopy invariants of time reversible periodic orbits. II: Towards applications. Zbl 0852.34039
Fiedler, Bernold; Heinze, Steffen
1996
Global attractors of one-dimensional parabolic equations: Sixteen examples. Zbl 0814.35056
Fiedler, Bernold
1994
Homoclinic period blow-up in reversible and conservative systems. Zbl 0762.34023
Vanderbauwhede, André; Fiedler, Bernold
1992
Dynamics of periodically forced parabolic equations on the circle. Zbl 0754.35066
Sandstede, Björn; Fiedler, Bernold
1992
Dynamics of bifurcations for variational problems with $$O(3)$$ equivariance: A Conley index approach. Zbl 0756.49003
Fiedler, Bernold; Mischaikow, Konstantin
1992
Homoclinic bifurcation at resonant eigenvalues. Zbl 0703.34050
Chow, Shui-Nee; Deng, Bo; Fiedler, Bernold
1990
Complicated dynamics of scalar reaction diffusion equations with a nonlocal term. Zbl 0726.35060
Fiedler, Bernold; Poláčik, Peter
1990
Connecting orbits in scalar reaction diffusion equations. II: The complete solution. Zbl 0699.35144
Brunovský, P.; Fiedler, B.
1989
A Poincaré-Bendixson theorem for scalar reaction diffusion equations. Zbl 0704.35070
Fiedler, Bernold; Mallet-Paret, John
1989
Connections between Morse sets for delay-differential equations. Zbl 0659.34077
Fiedler, Bernold; Maller-Paret, John
1989
Discrete Lyapunov functionals and $$\omega$$-limit sets. Zbl 0688.58041
Fiedler, Bernold
1989
Global decoupling of coupled symmetric oscillators. Zbl 0678.34038
Alexander, J. C.; Fiedler, B.
1989
Global bifurcation of periodic solutions with symmetry. Zbl 0644.34038
Fiedler, Bernold
1988
The dynamics of rotating waves in scalar reaction diffusion equations. Zbl 0696.35086
Angenent, S. B.; Fiedler, B.
1988
Connecting orbits in scalar reaction diffusion equations. Zbl 0679.35047
Brunovský, P.; Fiedler, B.
1988
Numerical pathfollowing beyond critical points in ODE models. Zbl 0617.65094
Deuflhard, P.; Fiedler, B.; Kunkel, P.
1987
Heteroclinic connections of stationary solutions of scalar reaction- diffusion equations. Zbl 0661.35050
Brunovský, P.; Fiedler, B.
1987
Numbers of zeros on invariant manifolds in reaction-diffusion equations. Zbl 0594.35056
Brunovský, Pavol; Fiedler, Bernold
1986
Global Hopf bifurcation of two-parameter flows. Zbl 0603.58015
Fiedler, Bernold
1986
Simplicity of zeros in scalar parabolic equations. Zbl 0549.35062
Brunovský, P.; Fiedler, B.
1986
Connections in scalar reaction diffusion equations with Neumann boundary condition. Zbl 0616.35044
Fiedler, B.; Brunovský, P.
1986
Global Hopf bifurcation for Volterra integral equations. Zbl 0605.45002
Fiedler, Bernold
1986
An index for global Hopf bifurcation in parabolic systems. Zbl 0554.35010
Fiedler, Bernold
1985
Global Hopf bifurcation in porous catalysts. Zbl 0528.35007
Fiedler, Bernold
1983
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#### Cited by 727 Authors

 38 Fiedler, Bernold 20 Rocha, Carlos 19 Zhu, Deming 18 Scheel, Arnd 15 Poláčik, Peter 13 Sandstede, Björn 9 Knobloch, Jürgen 9 Krawcewicz, Wieslaw Z. 9 Lamb, Jeroen S. W. 9 Li, Wenxue 8 Balanov, Zalman I. 8 Chepyzhov, Vladimir V. 8 Melbourne, Ian 7 Belhaq, Mohamed 7 Chung, Kwok-Wai 7 Fečkan, Michal 7 Homburg, Ale Jan 7 Valero, José 7 Wolfrum, Matthias 7 Wu, Jianhong 7 Wulff, Claudia 6 Ashwin, Peter 6 Brunovský, Pavol 6 Jin, Yinlai 6 Matthies, Karsten 6 Mielke, Alexander 6 Mischaikow, Konstantin 6 Fernandes da Silva Pimentel, Juliana 6 Qin, Bo-Wei 6 Rachinskii, Dmitrii I. 6 Rodríguez-Luis, Alejandro J. 5 Algaba, Antonio 5 Guo, Jong-Shenq 5 Hale, Jack Kenneth 5 Hooton, Edward W. 5 Kokubu, Hiroshi 5 Lakrad, Faouzi 5 Lappicy, Phillipo 5 Lu, Qiuying 5 Mallet-Paret, John Joseph 5 Naudot, Vincent 5 Nolasco de Carvalho, Alexandre 5 Rademacher, Jens Diederich Michael 5 Shen, Wenxian 5 Vishik, Marko Iosifovich 5 Wang, Ke 5 Zelik, Sergey V. 5 Zhang, Tiansi 4 Battelli, Flaviano 4 Champneys, Alan R. 4 Chechkin, Gregory Aleksandrovich 4 Deng, Bo 4 Fusco, Giorgio 4 Guo, Shangjiang 4 Lerman, Lev 4 Schneider, Isabelle 4 Su, Huan 4 van den Berg, Jan Bouwe 4 Vandervorst, Robertus C. A. M. 4 Wagenknecht, Thomas 4 Wang, Yi 4 Zhou, Dun 3 Angenent, Sigurd Bernardus 3 Bekmaganbetov, Kuanysh Abdrakhmanovich 3 Blyuss, Konstantin B. 3 Chen, Guanrong 3 Chen, Shuhui 3 Chen, Xu-Yan 3 Chen, Yangyang 3 de Rijk, Björn 3 Fahsi, Abdelhak 3 Freitas, Pedro 3 Gaeta, Giuseppe 3 Geng, Fengjie 3 Härterich, Jörg M. 3 Herrero, Miguel Ángel 3 Hövel, Philipp 3 Huang, Lihong 3 Hupkes, Hermen Jan 3 Joly, Romain 3 Kapustyan, Oleksiy V. 3 Kasyanov, Pavlo O. 3 Lauterbach, Reiner 3 Liebscher, Stefan 3 Matano, Hiroshi 3 Mei, Zhen 3 Postlethwaite, Claire M. 3 Prizzi, Martino 3 Rybakowski, Krzysztof P. 3 Scheurle, Jürgen 3 Schöll, Eckehard 3 Shih, Chih-Wen 3 Sze, Kam-Yim 3 Tsai, Je-Chiang 3 Valdebenito, Darío A. 3 Velázquez, Juan J. L. 3 Vishnevskii, Mikhail P. 3 Wakasa, Tohru 3 Wang, Wei 3 Zhang, Weipeng ...and 627 more Authors
all top 5

#### Cited in 148 Serials

 74 Journal of Differential Equations 47 Journal of Dynamics and Differential Equations 37 Physica D 37 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 21 Transactions of the American Mathematical Society 16 Archive for Rational Mechanics and Analysis 13 Discrete and Continuous Dynamical Systems 12 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 10 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 10 Chaos 9 Journal of Mathematical Biology 9 Nonlinear Dynamics 9 Communications in Nonlinear Science and Numerical Simulation 8 Chaos, Solitons and Fractals 8 Journal of Nonlinear Science 8 SIAM Journal on Applied Dynamical Systems 7 Discrete and Continuous Dynamical Systems. Series S 7 Nonlinear Analysis. Theory, Methods & Applications 6 Applied Mathematics and Computation 6 SIAM Journal on Mathematical Analysis 6 Discrete and Continuous Dynamical Systems. Series B 6 Communications on Pure and Applied Analysis 5 Journal of Mathematical Analysis and Applications 5 Nonlinearity 5 ZAMP. Zeitschrift für angewandte Mathematik und Physik 5 Proceedings of the American Mathematical Society 5 Dynamical Systems 5 Journal of Theoretical Biology 4 Applicable Analysis 4 Rocky Mountain Journal of Mathematics 4 Bulletin of Mathematical Biology 4 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 4 Dynamics and Stability of Systems 4 Journal de Mathématiques Pures et Appliquées. Neuvième Série 4 Regular and Chaotic Dynamics 3 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 3 Automatica 3 Journal of Computational and Applied Mathematics 3 Tohoku Mathematical Journal. Second Series 3 Ergodic Theory and Dynamical Systems 3 Systems & Control Letters 3 Applied Mathematics and Mechanics. (English Edition) 3 Chinese Annals of Mathematics. Series B 3 European Journal of Applied Mathematics 3 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 3 SIAM Journal on Applied Mathematics 3 Journal of Difference Equations and Applications 3 Acta Mathematica Sinica. English Series 3 Nonlinear Analysis. Real World Applications 3 Portugaliae Mathematica. Nova Série 3 São Paulo Journal of Mathematical Sciences 3 Journal of Geometric Mechanics 2 Communications on Pure and Applied Mathematics 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 BIT 2 Journal of Functional Analysis 2 Journal für die Reine und Angewandte Mathematik 2 Results in Mathematics 2 Siberian Mathematical Journal 2 Mathematical and Computer Modelling 2 Science in China. Series A 2 Acta Mathematica Sinica. New Series 2 Experimental Mathematics 2 Journal of Mathematical Sciences (New York) 2 Mathematical Problems in Engineering 2 Doklady Mathematics 2 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 2 Qualitative Theory of Dynamical Systems 2 Advances in Difference Equations 2 Mathematical Biosciences and Engineering 2 Science China. Technological Sciences 1 Computers & Mathematics with Applications 1 International Journal of Control 1 Israel Journal of Mathematics 1 Journal of Fluid Mechanics 1 Journal of the Franklin Institute 1 Journal of Mathematical Physics 1 Journal of the Mechanics and Physics of Solids 1 Journal of Statistical Physics 1 Mathematical Biosciences 1 Periodica Mathematica Hungarica 1 Physics Reports 1 Russian Mathematical Surveys 1 Computing 1 Indiana University Mathematics Journal 1 Integral Equations and Operator Theory 1 Kybernetika 1 Mathematische Annalen 1 Mathematische Nachrichten 1 Mathematica Slovaca 1 Meccanica 1 Quarterly of Applied Mathematics 1 Theoretical Computer Science 1 Transactions of the Moscow Mathematical Society 1 Topology and its Applications 1 Advances in Applied Mathematics 1 Acta Applicandae Mathematicae 1 Applied Numerical Mathematics 1 RAIRO. Modélisation Mathématique et Analyse Numérique 1 Probability Theory and Related Fields ...and 48 more Serials
all top 5

#### Cited in 37 Fields

 284 Dynamical systems and ergodic theory (37-XX) 249 Ordinary differential equations (34-XX) 238 Partial differential equations (35-XX) 76 Biology and other natural sciences (92-XX) 34 Numerical analysis (65-XX) 32 Systems theory; control (93-XX) 23 Global analysis, analysis on manifolds (58-XX) 21 Mechanics of particles and systems (70-XX) 20 Fluid mechanics (76-XX) 11 Combinatorics (05-XX) 11 Probability theory and stochastic processes (60-XX) 11 Information and communication theory, circuits (94-XX) 10 Operator theory (47-XX) 10 Optics, electromagnetic theory (78-XX) 10 Statistical mechanics, structure of matter (82-XX) 8 Difference and functional equations (39-XX) 8 Mechanics of deformable solids (74-XX) 5 Manifolds and cell complexes (57-XX) 4 Differential geometry (53-XX) 4 Algebraic topology (55-XX) 4 Computer science (68-XX) 4 Classical thermodynamics, heat transfer (80-XX) 3 Integral equations (45-XX) 3 Quantum theory (81-XX) 3 Operations research, mathematical programming (90-XX) 2 History and biography (01-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 General topology (54-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 General and overarching topics; collections (00-XX) 1 Field theory and polynomials (12-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Group theory and generalizations (20-XX) 1 Real functions (26-XX) 1 Approximations and expansions (41-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Relativity and gravitational theory (83-XX)

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