Edit Profile (opens in new tab) Fiedler, Bernold Co-Author Distance 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: 106 Publications since 1983, including 3 Books and 6 Additional arXiv Preprints 8 Contributions as Editor Biographic References: 1 Publication Co-Authors: 75 Co-Authors with 97 Joint Publications 2,680 Co-Co-Authors all top 5 Co-Authors 17 single-authored 20 Rocha, Carlos 9 Liebscher, Stefan 6 Brunovský, Pavol 4 Mochizuki, Atsushi 4 Sandstede, Björn 4 Schuppert, Andreas A. 4 Vishik, Marko Iosifovich 3 Afendikov, Andrei Leonidovich 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 Brehm, Bernhard 2 Gedeon, Tomáš 2 Gröger, Konrad 2 Guo, Jong-Shenq 2 Heinze, Steffen 2 Hell, Juliette 2 Hsu, Szebi 2 Kunkel, Peter 2 Kurosawa, Gen 2 Mallet-Paret, John Joseph 2 Poláčik, Peter 2 Rand, Richard H. 2 Sah, Si Mohamed 2 Saito, Daisuke 2 Schneider, Isabelle 2 Sprekels, Jürgen 2 Stuke, Hannes 2 Tsai, Je-Chiang 2 Turaev, Dmitry V. 1 Angenent, Sigurd Bernardus 1 Behrends, Ehrhard 1 Ben-Gal, Nitsan 1 Buchner, Johannes 1 Castañeda, Pablo 1 Dangelmayr, Gerhard 1 de Wolff, Babette A. J. 1 Deng, Bo 1 Deuflhard, Peter 1 Fila, Marek 1 Grotta Ragazzo, Clodoaldo 1 Haugland, Sindre W. 1 Houssni, Mohamed 1 Jangle, Nihar 1 Karnauhova, Anna 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 Rademacher, Jens Diederich Michael 1 Rendall, Alan D. 1 Salazar, Domingo 1 Scheurle, Jürgen 1 Schimansky-Geier, Lutz 1 Shayak, B. 1 Solà-Morales, Joan 1 Vanderbauwhede, Andre L. 1 Väth, Martin 1 Wulff, Claudia all top 5 Serials 12 Journal of Differential Equations 10 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 Pitman Research Notes in Mathematics Series 1 World Scientific Lecture Notes in Complex Systems 1 Networks and Heterogeneous Media 1 Nonlinear Analysis. Theory, Methods & Applications all top 5 Fields 64 Partial differential equations (35-XX) 61 Dynamical systems and ergodic theory (37-XX) 39 Ordinary differential equations (34-XX) 14 Biology and other natural sciences (92-XX) 10 General and overarching topics; collections (00-XX) 9 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) 2 Relativity and gravitational theory (83-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 Operations research, mathematical programming (90-XX) 1 Information and communication theory, circuits (94-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 92 Publications have been cited 1,192 times in 674 Documents Cited by ▼ Year ▼ Homoclinic bifurcation at resonant eigenvalues. Zbl 0703.34050 Chow, Shui-Nee; Deng, Bo; Fiedler, Bernold 72 1990 Heteroclinic orbits of semilinear parabolic equations. Zbl 0849.35056 Fiedler, Bernold; Rocha, Carlos 61 1996 Homoclinic period blow-up in reversible and conservative systems. Zbl 0762.34023 Vanderbauwhede, André; Fiedler, Bernold 55 1992 Connecting orbits in scalar reaction diffusion equations. II: The complete solution. Zbl 0699.35144 Brunovský, P.; Fiedler, B. 54 1989 A Poincaré-Bendixson theorem for scalar reaction diffusion equations. Zbl 0704.35070 Fiedler, Bernold; Mallet-Paret, John 48 1989 Global bifurcation of periodic solutions with symmetry. Zbl 0644.34038 Fiedler, Bernold 46 1988 Connecting orbits in scalar reaction diffusion equations. Zbl 0679.35047 Brunovský, P.; Fiedler, B. 45 1988 Spatio-temporal dynamics of reaction-diffusion patterns. Zbl 1082.37004 Fiedler, Bernold; Scheel, Arnd 43 2003 The dynamics of rotating waves in scalar reaction diffusion equations. Zbl 0696.35086 Angenent, S. B.; Fiedler, B. 42 1988 Orbit equivalence of global attractors of semilinear parabolic differential equations. Zbl 0932.37065 Fiedler, Bernold; Rocha, Carlos 37 2000 Complicated dynamics of scalar reaction diffusion equations with a nonlocal term. Zbl 0726.35060 Fiedler, Bernold; Poláčik, Peter 34 1990 Numbers of zeros on invariant manifolds in reaction-diffusion equations. Zbl 0594.35056 Brunovský, Pavol; Fiedler, Bernold 33 1986 Bifurcation from relative equilibria of noncompact group actions: Skew products, meanders, and drifts. Zbl 0870.58014 Fiedler, Bernold; Sandstede, Björn; Scheel, Arnd; Wulff, Claudia 29 1996 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 28 2000 Discretization of homoclinic orbits, rapid forcing and “invisible” chaos. Zbl 0923.34049 Fiedler, Bernold; Scheurle, Jürgen 26 1996 Realization of meander permutations by boundary value problems. Zbl 0935.34018 Fiedler, Bernold; Rocha, Carlos 23 1999 Dynamics of periodically forced parabolic equations on the circle. Zbl 0754.35066 Sandstede, Björn; Fiedler, Bernold 19 1992 Delay stabilization of periodic orbits in coupled oscillator systems. Zbl 1201.34103 Fiedler, B.; Flunkert, V.; Hövel, P.; Schöll, E. 18 2010 Heteroclinic orbits between rotating waves of semilinear parabolic equations on the circle. Zbl 1064.35076 Fiedler, Bernold; Rocha, Carlos; Wolfrum, Matthias 18 2004 Connections between Morse sets for delay-differential equations. Zbl 0659.34077 Fiedler, Bernold; Maller-Paret, John 17 1989 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 17 2013 Generic Hopf bifurcation from lines of equilibria without parameters. I: Theory. Zbl 0978.34035 Fiedler, Bernold; Liebscher, Stefan; Alexander, J. C. 15 2000 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 15 2013 Generic Hopf bifurcation from lines of equilibria without parameters. III. Binary oscillations. Zbl 1090.37556 Fiedler, Bernold; Liebscher, Stefan; Alexander, J. C. 14 2000 Dynamics of nonlinear waves in dissipative systems: reduction, bifurcation and stability. Zbl 0866.35002 Dangelmayr, Gerhard; Fiedler, Bernold; Kirchgässner, Klaus; Mielke, Alexander 14 1996 Global attractors of one-dimensional parabolic equations: Sixteen examples. Zbl 0814.35056 Fiedler, Bernold 14 1994 Basins of attraction in strongly damped coupled mechanical oscillators: A global example. Zbl 0919.70012 Fiedler, Bernold; Belhaq, Mohamed; Houssni, Mohamed 13 1999 Quantitative homogenization of global attractors for reaction-diffusion systems with rapidly oscillating terms. Zbl 1135.35315 Fiedler, Bernold; Vishik, Mark I. 13 2003 Connectivity and design of planar global attractors of Sturm type. II: Connection graphs. Zbl 1179.35069 Fiedler, Bernold; Rocha, Carlos 12 2008 An index for global Hopf bifurcation in parabolic systems. Zbl 0554.35010 Fiedler, Bernold 12 1985 Connectivity and design of planar global attractors of Sturm type. I: Bipolar orientations and Hamiltonian paths. Zbl 1201.37102 Fiedler, Bernold; Rocha, Carlos 12 2009 Connectivity and design of planar global attractors of Sturm type. III: Small and platonic examples. Zbl 1204.35106 Fiedler, Bernold; Rocha, Carlos 12 2010 Large patterns of elliptic systems in infinite cylinders. Zbl 0917.35011 Fiedler, Bernold; Scheel, Arnd; Vishik, Mark I. 11 1998 Quantitative homogenization of analytic semigroups and reaction-diffusion equations with Diophantine spatial frequencies. Zbl 1036.35022 Fiedler, Bernold; Vishik, Mark I. 11 2001 Generic Hopf bifurcation from lines of equilibria without parameters: II. Systems of viscous hyperbolic balance laws. Zbl 0980.35098 Fiedler, Bernold; Liebscher, Stefan 10 2000 Quantitative homogenization of global attractors for hyperbolic wave equations with rapidly oscillating coefficients. Zbl 1055.35025 Fiedler, B.; Vishik, M. I. 10 2002 Global Hopf bifurcation of two-parameter flows. Zbl 0603.58015 Fiedler, Bernold 10 1986 Dynamics of bifurcations for variational problems with \(O(3)\) equivariance: A Conley index approach. Zbl 0756.49003 Fiedler, Bernold; Mischaikow, Konstantin 10 1992 Do global attractors depend on boundary conditions? Zbl 0855.58053 Fiedler, Bernold 9 1996 Normal forms, resonances, and meandering tip motions near relative equilibria of Euclidean group actions. Zbl 0957.37026 Fiedler, Bernold; Turaev, Dmitry 9 1998 Handbook of dynamical systems. Volume 2. Zbl 0982.37002 9 2002 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 9 2008 Multiplicity of rotating spirals under curvature flows with normal tip motion. Zbl 1063.34001 Fiedler, Bernold; Guo, Jong-Shenq; Tsai, Je-Chiang 9 2004 A class of convergent neural network dynamics. Zbl 0944.34039 Fiedler, Bernold; Gedeon, Tomáš 8 1998 Coalescence of reversible homoclinic orbits causes elliptic resonance. Zbl 0876.34057 Fiedler, Bernold; Turaev, Dimitry 8 1996 An explicit Lyapunov function for reflection symmetric parabolic partial differential equations on the circle. Zbl 1307.35058 Fiedler, B.; Grotta-Ragazzo, C.; Rocha, C. 8 2014 Schoenflies spheres as boundaries of bounded unstable manifolds in gradient Sturm systems. Zbl 1375.35259 Fiedler, Bernold; Rocha, Carlos 8 2015 Sturm 3-ball global attractors 3: examples of Thom-Smale complexes. Zbl 1396.37036 Fiedler, Bernold; Rocha, Carlos 8 2018 Sensitivity of chemical reaction networks: A structural approach. 3. regular multimolecular systems. Zbl 1388.82017 Brehm, Bernhard; Fiedler, Bernold 7 2018 Rotating spirals of curvature flows: a center manifold approach. Zbl 1223.37110 Fiedler, Bernold; Guo, Jong-Shenq; Tsai, Je-Chiang 7 2006 Nonlinear Sturm global attractors: unstable manifold decompositions as regular CW-complexes. Zbl 1327.35194 Fiedler, Bernold; Rocha, Carlos 7 2014 A permutation characterization of Sturm global attractors of Hamiltonian type. Zbl 1233.35042 Fiedler, Bernold; Rocha, Carlos; Wolfrum, Matthias 6 2012 A Lyapunov function for tridiagonal competitive-cooperative systems. Zbl 0922.34041 Fiedler, Bernold; Gedeon, Tomás 6 1999 Delayed feedback control of a delay equation at Hopf bifurcation. Zbl 1358.34079 Fiedler, Bernold; Muniz Oliva, Sergio Muniz 6 2016 A Lyapunov function for fully nonlinear parabolic equations in one spatial variable. Zbl 1415.35155 Lappicy, Phillipo; Fiedler, Bernold 6 2019 Simplicity of zeros in scalar parabolic equations. Zbl 0549.35062 Brunovský, P.; Fiedler, B. 5 1986 Discrete Lyapunov functionals and \(\omega\)-limit sets. Zbl 0688.58041 Fiedler, Bernold 5 1989 Sensitivity of chemical reaction networks: a structural approach. 2. Regular monomolecular systems. Zbl 1333.94079 Fiedler, Bernold; Mochizuki, Atsushi 5 2015 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 5 2020 Sturm global attractors for \(S^1\)-equivariant parabolic equations. Zbl 1262.35053 Fiedler, Bernold; Rocha, Carlos; Wolfrum, Matthias 5 2012 Sturm 3-ball global attractors. 1: Thom-Smale complexes and meanders. Zbl 1408.37027 Fiedler, Bernold; Rocha, Carlos 5 2018 Non-periodicity in chemostat equations: a multi-dimensional negative Bendixson-Dulac criterion. Zbl 1231.92061 Fiedler, Bernold; Hsu, Sze-Bi 4 2009 Global pathfollowing of homoclinic orbits in twoparameter flows. Zbl 0866.35004 Fiedler, B. 4 1996 Delay stabilization of rotating waves without odd number limitation. Zbl 1160.37429 Fiedler, Bernold; Flunkert, Valentin; Georgi, Marc; Hövel, Philipp; Schöll, Eckehard 4 2008 Sensitivity of chemical reaction networks: a structural approach. 1. Examples and the carbon metabolic network. Zbl 1412.92098 Mochizuki, Atsushi; Fiedler, Bernold 4 2015 Global Hopf bifurcation in porous catalysts. Zbl 0528.35007 Fiedler, Bernold 3 1983 Periods of discretized linear Anosov maps. Zbl 0915.58075 Behrends, Ehrhard; Fiedler, Bernold 3 1998 Roots and centralizers of Anosov diffeomorphisms on tori. Zbl 1097.37015 Fiedler, Bernold 3 2005 Sturm 3-ball global attractors 2: design of Thom-Smale complexes. Zbl 1423.35040 Fiedler, Bernold; Rocha, Carlos 3 2019 Analysis and control of complex nonlinear processes in physics, chemistry and biology. Zbl 1110.82004 2 2007 Homotopy invariants of time reversible periodic orbits. I: Theory. Zbl 0852.34038 Fiedler, Bernold; Heinze, Steffen 2 1996 Global Hopf bifurcation for Volterra integral equations. Zbl 0605.45002 Fiedler, Bernold 2 1986 Connections in scalar reaction diffusion equations with Neumann boundary condition. Zbl 0616.35044 Fiedler, B.; Brunovský, P. 2 1986 Anisotropic Einstein data with isotropic non negative prescribed scalar curvature. Zbl 1332.35358 Fiedler, Bernold; Hell, Juliette; Smith, Brian 2 2015 Rainbow meanders and Cartesian billiards. Zbl 1333.37015 Fiedler, Bernold; Castañeda, Pablo 2 2012 Stabilized rapid oscillations in a delay equation: feedback control by a small resonant delay. Zbl 1450.34048 Fiedler, Bernold; Schneider, Isabelle 2 2020 Global Hopf bifurcation in networks with fast feedback cycles. Zbl 1454.34060 Fiedler, Bernold 2 2021 Heteroclinic connections of stationary solutions of scalar reaction- diffusion equations. Zbl 0661.35050 Brunovský, P.; Fiedler, B. 1 1987 Global decoupling of coupled symmetric oscillators. Zbl 0678.34038 Alexander, J. C.; Fiedler, B. 1 1989 Spiral wave dynamics: reaction and diffusion versus kinematics. Zbl 1126.80007 Fiedler, Bernold; Georgi, Marc; Jangle, Nihar 1 2007 Plane Kolmogorov flows and Takens-Bogdanov bifurcation without parameters: the singly reversible case. Zbl 1233.37054 Afendikov, Andrei; Fiedler, Bernold; Liebscher, Stefan 1 2011 Homotopy invariants of time reversible periodic orbits. II: Towards applications. Zbl 0852.34039 Fiedler, Bernold; Heinze, Steffen 1 1996 Takens-Bogdanov bifurcations without parameters and oscillatory shock profiles. Zbl 1198.37082 Fiedler, Bernold; Liebscher, Stefan 1 2001 Plane Kolmogorov flows and Takens-Bogdanov bifurcation without parameters: the doubly reversible case. Zbl 1173.35093 Afendikov, Andrei; Fiedler, Bernold; Liebscher, Stefan 1 2008 Numerical pathfollowing beyond critical points in ODE models. Zbl 0617.65094 Deuflhard, P.; Fiedler, B.; Kunkel, P. 1 1987 Thermically stable upscaling of an exothermic model reaction. (Thermisch stabiles Upscaling einer exothermen Modellreaktion.) Zbl 0867.76091 Fiedler, B.; Efendiev, M.; Schuppert, A. 1 1997 Upscaling of some exothermic reactions from chemical industry. Zbl 0887.92033 Efendiev, M. A.; Fiedler, B.; Schuppert, A. 1 1996 Global dynamics of blow-up profiles in one-dimensional reaction diffusion equations. Zbl 1132.35048 Fiedler, Bernold; Matano, Hiroshi 1 2007 Local identification of scalar hybrid models with tree structure. Zbl 1211.93040 Fiedler, Bernold; Schuppert, Andreas 1 2008 Bifurcations without parameters: Some ODE and PDE examples. Zbl 1037.34033 Fiedler, Bernold; Liebscher, Stefan 1 2002 Dynamics of piecewise-autonomous bistable parabolic equations. Zbl 1004.35069 Fiedler, Bernold; Rocha, Carlos; Salazar, Domingo; Solà-Morales, Joan 1 2002 Boundary orders and geometry of the signed Thom-Smale complex for Sturm global attractors. Zbl 1503.35040 Fiedler, Bernold; Rocha, Carlos 1 2022 Boundary orders and geometry of the signed Thom-Smale complex for Sturm global attractors. Zbl 1503.35040 Fiedler, Bernold; Rocha, Carlos 1 2022 Global Hopf bifurcation in networks with fast feedback cycles. Zbl 1454.34060 Fiedler, Bernold 2 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 5 2020 Stabilized rapid oscillations in a delay equation: feedback control by a small resonant delay. Zbl 1450.34048 Fiedler, Bernold; Schneider, Isabelle 2 2020 A Lyapunov function for fully nonlinear parabolic equations in one spatial variable. Zbl 1415.35155 Lappicy, Phillipo; Fiedler, Bernold 6 2019 Sturm 3-ball global attractors 2: design of Thom-Smale complexes. Zbl 1423.35040 Fiedler, Bernold; Rocha, Carlos 3 2019 Sturm 3-ball global attractors 3: examples of Thom-Smale complexes. Zbl 1396.37036 Fiedler, Bernold; Rocha, Carlos 8 2018 Sensitivity of chemical reaction networks: A structural approach. 3. regular multimolecular systems. Zbl 1388.82017 Brehm, Bernhard; Fiedler, Bernold 7 2018 Sturm 3-ball global attractors. 1: Thom-Smale complexes and meanders. Zbl 1408.37027 Fiedler, Bernold; Rocha, Carlos 5 2018 Delayed feedback control of a delay equation at Hopf bifurcation. Zbl 1358.34079 Fiedler, Bernold; Muniz Oliva, Sergio Muniz 6 2016 Schoenflies spheres as boundaries of bounded unstable manifolds in gradient Sturm systems. Zbl 1375.35259 Fiedler, Bernold; Rocha, Carlos 8 2015 Sensitivity of chemical reaction networks: a structural approach. 2. Regular monomolecular systems. Zbl 1333.94079 Fiedler, Bernold; Mochizuki, Atsushi 5 2015 Sensitivity of chemical reaction networks: a structural approach. 1. Examples and the carbon metabolic network. Zbl 1412.92098 Mochizuki, Atsushi; Fiedler, Bernold 4 2015 Anisotropic Einstein data with isotropic non negative prescribed scalar curvature. Zbl 1332.35358 Fiedler, Bernold; Hell, Juliette; Smith, Brian 2 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. 8 2014 Nonlinear Sturm global attractors: unstable manifold decompositions as regular CW-complexes. Zbl 1327.35194 Fiedler, Bernold; Rocha, Carlos 7 2014 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 17 2013 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 15 2013 A permutation characterization of Sturm global attractors of Hamiltonian type. Zbl 1233.35042 Fiedler, Bernold; Rocha, Carlos; Wolfrum, Matthias 6 2012 Sturm global attractors for \(S^1\)-equivariant parabolic equations. Zbl 1262.35053 Fiedler, Bernold; Rocha, Carlos; Wolfrum, Matthias 5 2012 Rainbow meanders and Cartesian billiards. Zbl 1333.37015 Fiedler, Bernold; Castañeda, Pablo 2 2012 Plane Kolmogorov flows and Takens-Bogdanov bifurcation without parameters: the singly reversible case. Zbl 1233.37054 Afendikov, Andrei; Fiedler, Bernold; Liebscher, Stefan 1 2011 Delay stabilization of periodic orbits in coupled oscillator systems. Zbl 1201.34103 Fiedler, B.; Flunkert, V.; Hövel, P.; Schöll, E. 18 2010 Connectivity and design of planar global attractors of Sturm type. III: Small and platonic examples. Zbl 1204.35106 Fiedler, Bernold; Rocha, Carlos 12 2010 Connectivity and design of planar global attractors of Sturm type. I: Bipolar orientations and Hamiltonian paths. Zbl 1201.37102 Fiedler, Bernold; Rocha, Carlos 12 2009 Non-periodicity in chemostat equations: a multi-dimensional negative Bendixson-Dulac criterion. Zbl 1231.92061 Fiedler, Bernold; Hsu, Sze-Bi 4 2009 Connectivity and design of planar global attractors of Sturm type. II: Connection graphs. Zbl 1179.35069 Fiedler, Bernold; Rocha, Carlos 12 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 9 2008 Delay stabilization of rotating waves without odd number limitation. Zbl 1160.37429 Fiedler, Bernold; Flunkert, Valentin; Georgi, Marc; Hövel, Philipp; Schöll, Eckehard 4 2008 Plane Kolmogorov flows and Takens-Bogdanov bifurcation without parameters: the doubly reversible case. Zbl 1173.35093 Afendikov, Andrei; Fiedler, Bernold; Liebscher, Stefan 1 2008 Local identification of scalar hybrid models with tree structure. Zbl 1211.93040 Fiedler, Bernold; Schuppert, Andreas 1 2008 Analysis and control of complex nonlinear processes in physics, chemistry and biology. Zbl 1110.82004 2 2007 Spiral wave dynamics: reaction and diffusion versus kinematics. Zbl 1126.80007 Fiedler, Bernold; Georgi, Marc; Jangle, Nihar 1 2007 Global dynamics of blow-up profiles in one-dimensional reaction diffusion equations. Zbl 1132.35048 Fiedler, Bernold; Matano, Hiroshi 1 2007 Rotating spirals of curvature flows: a center manifold approach. Zbl 1223.37110 Fiedler, Bernold; Guo, Jong-Shenq; Tsai, Je-Chiang 7 2006 Roots and centralizers of Anosov diffeomorphisms on tori. Zbl 1097.37015 Fiedler, Bernold 3 2005 Heteroclinic orbits between rotating waves of semilinear parabolic equations on the circle. Zbl 1064.35076 Fiedler, Bernold; Rocha, Carlos; Wolfrum, Matthias 18 2004 Multiplicity of rotating spirals under curvature flows with normal tip motion. Zbl 1063.34001 Fiedler, Bernold; Guo, Jong-Shenq; Tsai, Je-Chiang 9 2004 Spatio-temporal dynamics of reaction-diffusion patterns. Zbl 1082.37004 Fiedler, Bernold; Scheel, Arnd 43 2003 Quantitative homogenization of global attractors for reaction-diffusion systems with rapidly oscillating terms. Zbl 1135.35315 Fiedler, Bernold; Vishik, Mark I. 13 2003 Quantitative homogenization of global attractors for hyperbolic wave equations with rapidly oscillating coefficients. Zbl 1055.35025 Fiedler, B.; Vishik, M. I. 10 2002 Handbook of dynamical systems. Volume 2. Zbl 0982.37002 9 2002 Bifurcations without parameters: Some ODE and PDE examples. Zbl 1037.34033 Fiedler, Bernold; Liebscher, Stefan 1 2002 Dynamics of piecewise-autonomous bistable parabolic equations. Zbl 1004.35069 Fiedler, Bernold; Rocha, Carlos; Salazar, Domingo; Solà-Morales, Joan 1 2002 Quantitative homogenization of analytic semigroups and reaction-diffusion equations with Diophantine spatial frequencies. Zbl 1036.35022 Fiedler, Bernold; Vishik, Mark I. 11 2001 Takens-Bogdanov bifurcations without parameters and oscillatory shock profiles. Zbl 1198.37082 Fiedler, Bernold; Liebscher, Stefan 1 2001 Orbit equivalence of global attractors of semilinear parabolic differential equations. Zbl 0932.37065 Fiedler, Bernold; Rocha, Carlos 37 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 28 2000 Generic Hopf bifurcation from lines of equilibria without parameters. I: Theory. Zbl 0978.34035 Fiedler, Bernold; Liebscher, Stefan; Alexander, J. C. 15 2000 Generic Hopf bifurcation from lines of equilibria without parameters. III. Binary oscillations. Zbl 1090.37556 Fiedler, Bernold; Liebscher, Stefan; Alexander, J. C. 14 2000 Generic Hopf bifurcation from lines of equilibria without parameters: II. Systems of viscous hyperbolic balance laws. Zbl 0980.35098 Fiedler, Bernold; Liebscher, Stefan 10 2000 Realization of meander permutations by boundary value problems. Zbl 0935.34018 Fiedler, Bernold; Rocha, Carlos 23 1999 Basins of attraction in strongly damped coupled mechanical oscillators: A global example. Zbl 0919.70012 Fiedler, Bernold; Belhaq, Mohamed; Houssni, Mohamed 13 1999 A Lyapunov function for tridiagonal competitive-cooperative systems. Zbl 0922.34041 Fiedler, Bernold; Gedeon, Tomás 6 1999 Large patterns of elliptic systems in infinite cylinders. Zbl 0917.35011 Fiedler, Bernold; Scheel, Arnd; Vishik, Mark I. 11 1998 Normal forms, resonances, and meandering tip motions near relative equilibria of Euclidean group actions. Zbl 0957.37026 Fiedler, Bernold; Turaev, Dmitry 9 1998 A class of convergent neural network dynamics. Zbl 0944.34039 Fiedler, Bernold; Gedeon, Tomáš 8 1998 Periods of discretized linear Anosov maps. Zbl 0915.58075 Behrends, Ehrhard; Fiedler, Bernold 3 1998 Thermically stable upscaling of an exothermic model reaction. (Thermisch stabiles Upscaling einer exothermen Modellreaktion.) Zbl 0867.76091 Fiedler, B.; Efendiev, M.; Schuppert, A. 1 1997 Heteroclinic orbits of semilinear parabolic equations. Zbl 0849.35056 Fiedler, Bernold; Rocha, Carlos 61 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 29 1996 Discretization of homoclinic orbits, rapid forcing and “invisible” chaos. Zbl 0923.34049 Fiedler, Bernold; Scheurle, Jürgen 26 1996 Dynamics of nonlinear waves in dissipative systems: reduction, bifurcation and stability. Zbl 0866.35002 Dangelmayr, Gerhard; Fiedler, Bernold; Kirchgässner, Klaus; Mielke, Alexander 14 1996 Do global attractors depend on boundary conditions? Zbl 0855.58053 Fiedler, Bernold 9 1996 Coalescence of reversible homoclinic orbits causes elliptic resonance. Zbl 0876.34057 Fiedler, Bernold; Turaev, Dimitry 8 1996 Global pathfollowing of homoclinic orbits in twoparameter flows. Zbl 0866.35004 Fiedler, B. 4 1996 Homotopy invariants of time reversible periodic orbits. I: Theory. Zbl 0852.34038 Fiedler, Bernold; Heinze, Steffen 2 1996 Homotopy invariants of time reversible periodic orbits. II: Towards applications. Zbl 0852.34039 Fiedler, Bernold; Heinze, Steffen 1 1996 Upscaling of some exothermic reactions from chemical industry. Zbl 0887.92033 Efendiev, M. A.; Fiedler, B.; Schuppert, A. 1 1996 Global attractors of one-dimensional parabolic equations: Sixteen examples. Zbl 0814.35056 Fiedler, Bernold 14 1994 Homoclinic period blow-up in reversible and conservative systems. Zbl 0762.34023 Vanderbauwhede, André; Fiedler, Bernold 55 1992 Dynamics of periodically forced parabolic equations on the circle. Zbl 0754.35066 Sandstede, Björn; Fiedler, Bernold 19 1992 Dynamics of bifurcations for variational problems with \(O(3)\) equivariance: A Conley index approach. Zbl 0756.49003 Fiedler, Bernold; Mischaikow, Konstantin 10 1992 Homoclinic bifurcation at resonant eigenvalues. Zbl 0703.34050 Chow, Shui-Nee; Deng, Bo; Fiedler, Bernold 72 1990 Complicated dynamics of scalar reaction diffusion equations with a nonlocal term. Zbl 0726.35060 Fiedler, Bernold; Poláčik, Peter 34 1990 Connecting orbits in scalar reaction diffusion equations. II: The complete solution. Zbl 0699.35144 Brunovský, P.; Fiedler, B. 54 1989 A Poincaré-Bendixson theorem for scalar reaction diffusion equations. Zbl 0704.35070 Fiedler, Bernold; Mallet-Paret, John 48 1989 Connections between Morse sets for delay-differential equations. Zbl 0659.34077 Fiedler, Bernold; Maller-Paret, John 17 1989 Discrete Lyapunov functionals and \(\omega\)-limit sets. Zbl 0688.58041 Fiedler, Bernold 5 1989 Global decoupling of coupled symmetric oscillators. Zbl 0678.34038 Alexander, J. C.; Fiedler, B. 1 1989 Global bifurcation of periodic solutions with symmetry. Zbl 0644.34038 Fiedler, Bernold 46 1988 Connecting orbits in scalar reaction diffusion equations. Zbl 0679.35047 Brunovský, P.; Fiedler, B. 45 1988 The dynamics of rotating waves in scalar reaction diffusion equations. Zbl 0696.35086 Angenent, S. B.; Fiedler, B. 42 1988 Heteroclinic connections of stationary solutions of scalar reaction- diffusion equations. Zbl 0661.35050 Brunovský, P.; Fiedler, B. 1 1987 Numerical pathfollowing beyond critical points in ODE models. Zbl 0617.65094 Deuflhard, P.; Fiedler, B.; Kunkel, P. 1 1987 Numbers of zeros on invariant manifolds in reaction-diffusion equations. Zbl 0594.35056 Brunovský, Pavol; Fiedler, Bernold 33 1986 Global Hopf bifurcation of two-parameter flows. Zbl 0603.58015 Fiedler, Bernold 10 1986 Simplicity of zeros in scalar parabolic equations. Zbl 0549.35062 Brunovský, P.; Fiedler, B. 5 1986 Global Hopf bifurcation for Volterra integral equations. Zbl 0605.45002 Fiedler, Bernold 2 1986 Connections in scalar reaction diffusion equations with Neumann boundary condition. Zbl 0616.35044 Fiedler, B.; Brunovský, P. 2 1986 An index for global Hopf bifurcation in parabolic systems. Zbl 0554.35010 Fiedler, Bernold 12 1985 Global Hopf bifurcation in porous catalysts. Zbl 0528.35007 Fiedler, Bernold 3 1983 all cited Publications top 5 cited Publications all top 5 Cited by 829 Authors 41 Fiedler, Bernold 25 Scheel, Arnd 22 Rocha, Carlos 19 Zhu, Deming 16 Poláčik, Peter 15 Sandstede, Björn 10 Chepyzhov, Vladimir V. 10 Krawcewicz, Wieslaw Z. 9 Knobloch, Jürgen 9 Lamb, Jeroen S. W. 9 Li, Wenxue 8 Balanov, Zalman I. 8 Melbourne, Ian 8 Mischaikow, Konstantin 8 Valero, José 8 Wang, Yi 8 Wu, Jianhong 7 Belhaq, Mohamed 7 Brunovský, Pavol 7 Chung, Kwok-Wai 7 Fečkan, Michal 7 Homburg, Ale Jan 7 Lappicy, Phillipo 7 Mielke, Alexander 7 Rademacher, Jens Diederich Michael 7 Wolfrum, Matthias 7 Wulff, Claudia 7 Zelik, Sergey V. 6 Ashwin, Peter 6 Jin, Yinlai 6 Matthies, Karsten 6 Postlethwaite, Claire M. 6 Qin, Bo-Wei 6 Rachinskii, Dmitrii I. 6 Rodríguez-Luis, Alejandro J. 6 Schneider, Isabelle 6 Shen, Wenxian 6 Vishik, Marko Iosifovich 5 Algaba, Antonio 5 Avery, Montie 5 Champneys, Alan R. 5 Chechkin, Gregory Aleksandrovich 5 de Wolff, Babette A. J. 5 Guo, Jong-Shenq 5 Hale, Jack Kenneth 5 Hooton, Edward W. 5 Kokubu, Hiroshi 5 Lerman, Lev 5 Lu, Qiuying 5 Mallet-Paret, John Joseph 5 Naudot, Vincent 5 Nolasco de Carvalho, Alexandre 5 Fernandes da Silva Pimentel, Juliana 5 Valdebenito, Darío A. 5 Vandervorst, Robertus C. A. M. 5 Wang, Ke 5 Zhang, Tiansi 5 Zhou, Dun 4 Battelli, Flaviano 4 Bekmaganbetov, Kuanysh Abdrakhmanovich 4 Deng, Bo 4 Fusco, Giorgio 4 Guo, Shangjiang 4 Joly, Romain 4 Lakrad, Faouzi 4 Schöll, Eckehard 4 Su, Huan 4 Tsai, Je-Chiang 4 van den Berg, Jan Bouwe 4 Wagenknecht, Thomas 4 Yagasaki, Kazuyuki 3 Angenent, Sigurd Bernardus 3 Beyn, Wolf-Jürgen 3 Blyuss, Konstantin B. 3 Chen, Guanrong 3 Chen, Shuhui 3 Chen, Xu-Yan 3 Chen, Yangyang 3 Czaja, Radosław 3 Dai, Jia-Yuan 3 de Rijk, Björn 3 Fahsi, Abdelhak 3 Freitas, Pedro 3 Gaeta, Giuseppe 3 Geng, Fengjie 3 Goh, Ryan N. 3 Härterich, Jörg M. 3 Herrero, Miguel Ángel 3 Hövel, Philipp 3 Huang, Lihong 3 Hupkes, Hermen Jan 3 Kalies, William D. 3 Kapustyan, Oleksiy V. 3 Kasyanov, Pavlo O. 3 Kobayashi, Koichi 3 Krauskopf, Bernd 3 Lauterbach, Reiner 3 Liebscher, Stefan 3 Liu, Yan 3 Matano, Hiroshi ...and 729 more Authors all top 5 Cited in 164 Serials 78 Journal of Differential Equations 57 Journal of Dynamics and Differential Equations 40 Physica D 37 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 21 Transactions of the American Mathematical Society 17 Archive for Rational Mechanics and Analysis 14 SIAM Journal on Applied Dynamical Systems 13 Discrete and Continuous Dynamical Systems 12 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 10 Nonlinearity 10 Chaos, Solitons and Fractals 10 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 10 Chaos 9 Journal of Mathematical Biology 9 SIAM Journal on Mathematical Analysis 9 Nonlinear Dynamics 9 Communications in Nonlinear Science and Numerical Simulation 8 Journal of Nonlinear Science 7 Applied Mathematics and Computation 7 Dynamical Systems 7 Discrete and Continuous Dynamical Systems. Series B 7 Discrete and Continuous Dynamical Systems. Series S 7 Nonlinear Analysis. Theory, Methods & Applications 6 Journal of Mathematical Analysis and Applications 6 ZAMP. Zeitschrift für angewandte Mathematik und Physik 6 Bulletin of Mathematical Biology 6 Communications on Pure and Applied Analysis 5 Applicable Analysis 5 Proceedings of the American Mathematical Society 5 Journal of Theoretical Biology 4 Rocky Mountain Journal of Mathematics 4 Automatica 4 Journal of Computational and Applied Mathematics 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 SIAM Journal on Applied Mathematics 4 Regular and Chaotic Dynamics 3 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 3 Journal of Functional Analysis 3 Tôhoku 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 Journal of Mathematical Sciences (New York) 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 The European Physical Journal B. Condensed Matter and Complex Systems 3 São Paulo Journal of Mathematical Sciences 3 Journal of Geometric Mechanics 2 Communications on Pure and Applied Mathematics 2 Mathematical Biosciences 2 Russian Mathematical Surveys 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 BIT 2 Indiana University Mathematics Journal 2 Journal für die Reine und Angewandte Mathematik 2 Mathematische Nachrichten 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 International Journal of Robust and Nonlinear Control 2 Experimental Mathematics 2 Topological Methods in Nonlinear Analysis 2 Electronic Journal of Differential Equations (EJDE) 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. Mathematics 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 Methods in the Applied Sciences 1 Periodica Mathematica Hungarica 1 Physics Reports 1 Computing 1 Fundamenta Mathematicae 1 Integral Equations and Operator Theory 1 Kybernetika 1 Mathematische Annalen 1 Mathematica Slovaca 1 Meccanica 1 Memoirs of the American Mathematical Society 1 Quarterly of Applied Mathematics ...and 64 more Serials all top 5 Cited in 39 Fields 309 Dynamical systems and ergodic theory (37-XX) 278 Partial differential equations (35-XX) 271 Ordinary differential equations (34-XX) 93 Biology and other natural sciences (92-XX) 40 Systems theory; control (93-XX) 38 Numerical analysis (65-XX) 23 Global analysis, analysis on manifolds (58-XX) 21 Mechanics of particles and systems (70-XX) 21 Fluid mechanics (76-XX) 15 Probability theory and stochastic processes (60-XX) 14 Combinatorics (05-XX) 14 Information and communication theory, circuits (94-XX) 13 Operator theory (47-XX) 12 Statistical mechanics, structure of matter (82-XX) 11 Optics, electromagnetic theory (78-XX) 8 Difference and functional equations (39-XX) 8 Mechanics of deformable solids (74-XX) 7 Differential geometry (53-XX) 6 Operations research, mathematical programming (90-XX) 5 Manifolds and cell complexes (57-XX) 5 Computer science (68-XX) 5 Classical thermodynamics, heat transfer (80-XX) 4 Algebraic topology (55-XX) 3 Integral equations (45-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 3 Quantum theory (81-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 History and biography (01-XX) 2 General topology (54-XX) 1 General and overarching topics; collections (00-XX) 1 Order, lattices, ordered algebraic structures (06-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 Statistics (62-XX) 1 Relativity and gravitational theory (83-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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