Edit Profile (opens in new tab) Knobloch, Edgar Co-Author Distance Author ID: knobloch.edgar Published as: Knobloch, Edgar; Knobloch, E.; Knoblauch, Edgar more...less External Links: MGP · Wikidata · GND Documents Indexed: 190 Publications since 1977, including 1 Additional arXiv Preprint 2 Contributions as Editor Co-Authors: 103 Co-Authors with 160 Joint Publications 2,234 Co-Co-Authors all top 5 Co-Authors 20 single-authored 23 Julien, Keith A. 14 Bergeon, Alain 12 Mercader, Isabel 10 Tobias, Steven M. 10 Vega, José Manuel 9 Proctor, Michael Richard Edward 8 Batiste, Oriol 7 Weiss, Nigel O. 6 Alonso, Arantxa 6 Higuera, María J. 6 Hirschberg, P. 6 Moehlis, Jeff 6 Porter, Jeff 5 Crawford, John David 5 Net, Marta 5 Thiele, Uwe 4 Champneys, Alan R. 4 Dangelmayr, Gerhard 4 Golubitsky, Martin A. 4 Lo Jacono, David 4 Pierce, Robert D. 4 Silber, Mary 4 Spruit, H. C. 4 Toomre, Juri 3 Avitabile, Daniele 3 Beaume, Cédric 3 Callahan, T. K. 3 Deane, Anil E. 3 Favier, Benjamin 3 Goldstein, H. F. 3 Gomila, Damià 3 Kao, Hsien-Ching 3 Kirk, Vivien 3 Martel, Carlos 3 Prat, Joana d’Arc 3 Werne, Joseph 2 Archer, Andrew J. 2 Assemat, Pauline 2 Chini, Gregory P. 2 Clune, Thomas L. 2 da Costa, Luiz Nicolaci 2 Desroches, Mathieu 2 Gandhi, Punit 2 Houghton, S. M. 2 Liu, Chang 2 Moore, Daniel R. 2 Oldeman, Bart E. 2 Parra-Rivas, Pedro 2 Rucklidge, Alastair M. 2 Stewart, Ian Nicholas 2 Yochelis, Arik 1 Al Saadi, Fahad 1 Aurnou, Jonathan M. 1 Bardan, Gérald 1 Beltrame, Philippe 1 Calkins, Michael A. 1 Carter, Paul M. 1 De Luca, Jayme 1 Gelens, Lendert 1 Gomes, M. Gabriela M. 1 Grooms, Ian G. 1 Guckenheimer, John M. 1 Guervilly, Céline 1 Gurevich, Svetlana V. 1 Hänggi, Peter 1 Henry, Daniel 1 Hettel, J. 1 Holl, Max Philipp 1 Jamroz, Ben 1 Lloyd, David J. B. 1 Mahalov, Alex 1 Marques, Francisco 1 Marsden, Jerrold Eldon 1 Marti, Philippe 1 Mason, Joanne 1 Meseguer, Álvaro 1 Milliff, Ralph F. 1 Mojtabi, Abdelkader 1 Omel’chenko, Oleh E. 1 Ophaus, Lukas 1 Plumley, Meredith 1 Rademacher, Jens Diederich Michael 1 Riecke, Hermann 1 Rubio, Antonio M. 1 Rüdiger, Sten 1 Sandstede, Björn 1 Sharma, Manjul 1 Sneyd, James 1 Sprague, Michael A. 1 Stellmach, Stephan 1 Subramanian, Priya 1 Swift, James W. 1 Van Kan, Adrian 1 Vasil, Geoffrey M. 1 Wagenknecht, Thomas 1 Wechselberger, Martin 1 Weiss, Jeffrey B. 1 Wiesenfeld, K. A. 1 Wolfrum, Matthias 1 Worledge, Daniel ...and 3 more Co-Authors all top 5 Serials 37 Physica D 30 Journal of Fluid Mechanics 16 Physics of Fluids 9 Nonlinearity 8 Geophysical and Astrophysical Fluid Dynamics 8 SIAM Journal on Applied Dynamical Systems 7 Fluid Dynamics Research 6 IMA Journal of Applied Mathematics 4 Journal of Nonlinear Science 4 Chaos 3 Astronomy and Astrophysics 3 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 2 Journal of Statistical Physics 2 Physics Letters. A 2 Theoretical and Computational Fluid Dynamics 2 Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 2 Discrete and Continuous Dynamical Systems 2 Dynamical Systems 1 Applied Scientific Research 1 Astronomische Nachrichten 1 Astrophysics and Space Science 1 International Journal of Engineering Science 1 Journal of Mathematical Physics 1 Philosophical Transactions of the Royal Society of London. Ser. A 1 Quarterly of Applied Mathematics 1 Acta Applicandae Mathematicae 1 SIAM Review 1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Mathematical Modelling of Natural Phenomena 1 Discrete and Continuous Dynamical Systems. Series S 1 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 1 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences all top 5 Fields 122 Fluid mechanics (76-XX) 52 Dynamical systems and ergodic theory (37-XX) 44 Partial differential equations (35-XX) 27 Ordinary differential equations (34-XX) 14 Astronomy and astrophysics (85-XX) 11 Classical thermodynamics, heat transfer (80-XX) 7 Geophysics (86-XX) 6 Mechanics of particles and systems (70-XX) 5 Global analysis, analysis on manifolds (58-XX) 5 Statistical mechanics, structure of matter (82-XX) 5 Biology and other natural sciences (92-XX) 3 General and overarching topics; collections (00-XX) 3 Numerical analysis (65-XX) 3 Quantum theory (81-XX) 2 Mechanics of deformable solids (74-XX) 2 Optics, electromagnetic theory (78-XX) 1 History and biography (01-XX) 1 Probability theory and stochastic processes (60-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 162 Publications have been cited 1,978 times in 1,144 Documents Cited by ▼ Year ▼ Bifurctions, patterns and symmetry. Selected papers dedicated to the memory of John David Crawford. Zbl 0956.00057 118 2000 Snakes and ladders: localized states in the Swift-Hohenberg equation. Zbl 1236.35144 Burke, John; Knobloch, Edgar 78 2006 Homoclinic snaking: Structure and stability. Zbl 1163.37317 Burke, John; Knobloch, Edgar 66 2007 Symmetries and pattern selection in Rayleigh-Bénard convection. Zbl 0599.76098 Golubitsky, M.; Swift, J. W.; Knobloch, E. 53 1984 Numerical simulation of an asymptotically reduced system for rotationally constrained convection. Zbl 1119.76057 Sprague, Michael; Julien, Keith; Knobloch, Edgar; Werne, Joseph 48 2006 Thin liquid films on a slightly inclined heated plate. Zbl 1063.76032 Thiele, Uwe; Knobloch, Edgar 41 2004 To snake or not to snake in the planar Swift-Hohenberg equation. Zbl 1200.37014 Avitabile, Daniele; Lloyd, David J. B.; Burke, John; Knobloch, Edgar; Sandstede, Björn 39 2010 Convection in a rotating cylinder. I: Linear theory for moderate Prandtl numbers. Zbl 0796.76037 Goldstein, H. F.; Knobloch, E.; Mercader, I.; Net, M. 38 1993 Spatially localized structures in dissipative systems: open problems. Zbl 1139.35002 Knobloch, E. 37 2008 Pattern formation in three-dimensional reaction-diffusion systems. Zbl 0935.35065 Callahan, T. K.; Knobloch, E. 35 1999 Spatially localized binary-fluid convection. Zbl 1122.76029 Batiste, Oriol; Knobloch, Edgar; Alonso, Arantxa; Mercader, Isabel 35 2006 Nonlinear periodic convection in double-diffusive systems. Zbl 0478.76050 Knobloch, E.; Proctor, M. R. E. 33 1981 Convective and absolute instabilities of fluid flows in finite geometry. Zbl 0962.76526 Tobias, S. M.; Proctor, M. R. E.; Knobloch, E. 32 1998 Statistical and physical balances in low Rossby number Rayleigh-Bénard convection. Zbl 07649676 Julien, K.; Rubio, A. M.; Grooms, I.; Knobloch, E. 32 2012 Problems on time-varying domains: formulation, dynamics, and challenges. Zbl 1332.35004 Knobloch, E.; Krechetnikov, R. 30 2015 Symmetry and symmetry-breaking bifurcations in fluid dynamics. Zbl 0717.76007 Crawford, John David; Knobloch, Edgar 29 1991 A new class of equations for rotationally constrained flows. Zbl 0923.76338 Julien, Keith; Knobloch, Edgar; Werne, Joseph 27 1998 Oscillations in double-diffusive convection. Zbl 0475.76047 Da Costa, L. N.; Knobloch, E.; Weiss, N. O. 27 1981 When Shil’nikov meets Hopf in excitable systems. Zbl 1170.34025 Champneys, Alan R.; Kirk, Vivien; Knobloch, Edgar; Oldeman, Bart E.; Sneyd, James 27 2007 Generalized quasi-geostrophy for spatially anisotropic rotationally constrained flows. Zbl 1090.76077 Julien, Keith; Knobloch, Edgar; Milliff, Ralph; Werne, Joseph 26 2006 Bifurcations in fluctuating systems: The center-manifold approach. Zbl 0587.58033 Knobloch, E.; Wiesenfeld, K. A. 26 1983 Reduced models for fluid flows with strong constraints. Zbl 1144.81362 Julien, Keith; Knobloch, Edgar 26 2007 Amplitude equations for travelling wave convection. Zbl 0717.35070 Knobloch, E.; De Luca, J. 25 1990 Transitions to chaos in two-dimensional double-diffusive convection. Zbl 0612.76047 Knobloch, Edgar; Moore, Daniel R.; Toomre, Juri; Weiss, Nigel O. 23 1986 Hopf bifurcation on a square lattice. Zbl 0753.58021 Silber, Mary; Knobloch, Edgar 23 1991 Symmetry and instability in rotating hydrodynamic and magnetohydrodynamic flows. Zbl 1087.76043 Knobloch, Edgar 23 1996 Pattern selection in long-wavelength convection. Zbl 0699.76056 Knobloch, E. 22 1990 Boundary conditions as symmetry constraints. Zbl 0735.35007 Crawford, J. D.; Golubitsky, M.; Gomes, M. G. M.; Knobloch, E.; Stewart, I. N. 21 1991 The Takens-Bogdanov bifurcation with O(2)-symmetry. Zbl 0635.58032 Dangelmayr, G.; Knobloch, E. 20 1987 New type of complex dynamics in the \(1:2\) spatial resonance. Zbl 0979.70017 Porter, J.; Knobloch, E. 20 2001 Shilnikov-Hopf bifurcation. Zbl 0786.34052 Hirschberg, P.; Knobloch, E. 20 1993 Strongly nonlinear convection cells in a rapidly rotating fluid layer: The tilted \(f\)-plane. Zbl 0922.76192 Julien, Keith; Knobloch, Edgar 19 1998 The double Hopf bifurcation with 2:1 resonance. Zbl 0646.34042 Knobloch, E.; Proctor, M. R. E. 18 1988 Oscillatory and steady convection in a magnetic field. Zbl 0513.76078 Knobloch, E.; Weiss, N. O.; Da Costa, L. N. 18 1981 Dynamics of counterpropagating waves in parametrically forced systems. Zbl 0949.35019 Martel, Carlos; Knobloch, Edgar; Vega, José M. 18 2000 Front and back instability of a liquid film on a slightly inclined plate. Zbl 1186.76522 Thiele, Uwe; Knobloch, Edgar 17 2003 Hopf bifurcation with broken circular symmetry. Zbl 0731.58051 Dangelmayr, Gerhard; Knobloch, Edgar 17 1991 Fully nonlinear three-dimensional convection in a rapidly rotating layer. Zbl 1147.76426 Julien, Keith; Knobloch, Edgar 17 1999 Pattern selection in three-dimensional magnetoconvection. Zbl 0816.35109 Clune, Thomas; Knobloch, Edgar 16 1994 A nonlinear model for rotationally constrained convection with Ekman pumping. Zbl 1422.76165 Julien, Keith; Aurnou, Jonathan M.; Calkins, Michael A.; Knobloch, Edgar; Marti, Philippe; Stellmach, Stephan; Vasil, Geoffrey M. 15 2016 Defect-mediated snaking: a new growth mechanism for localized structures. Zbl 1213.37033 Ma, Y.-P.; Burke, J.; Knobloch, E. 15 2010 Convectons, anticonvectons and multiconvectons in binary fluid convection. Zbl 1225.76107 Mercader, Isabel; Batiste, Oriol; Alonso, Arantxa; Knobloch, Edgar 14 2011 Nearly inviscid Faraday waves in annular containers of moderately large aspect ratio. Zbl 1029.76017 Vega, José M.; Knobloch, Edgar; Martel, Carlos 14 2001 Convection in a rotating cylinder. II: Linear theory for low Prandtl numbers. Zbl 0800.76142 Goldstein, H. F.; Knobloch, E.; Mercader, I.; Net, M. 14 1994 Robust wall states in rapidly rotating Rayleigh-Bénard convection. Zbl 1460.76719 Favier, Benjamin; Knobloch, Edgar 14 2020 Three-dimensional doubly diffusive convectons: instability and transition to complex dynamics. Zbl 1419.76214 Beaume, Cédric; Bergeon, Alain; Knobloch, Edgar 14 2018 Nonlinear convection in a rotating layer: Amplitude expansions and normal forms. Zbl 0527.76038 Guckenheimer, J.; Knobloch, E. 13 1983 Rotating convection: recent developments. Zbl 1210.76077 Knobloch, Edgar 13 1998 Target patterns and spirals in planar reaction-diffusion systems. Zbl 0965.35084 Golubitsky, M.; Knobloch, E.; Stewart, I. 13 2000 On the modulational stability of traveling and standing water waves. Zbl 0830.76013 Pierce, R. D.; Knobloch, E. 13 1994 Spatially localized states in natural doubly diffusive convection. Zbl 1182.76055 Bergeon, A.; Knobloch, E. 13 2008 Natural doubly diffusive convection in three-dimensional enclosures. Zbl 1185.76049 Bergeon, A.; Knobloch, E. 13 2002 Robust heteroclinic cycles in two-dimensional Rayleigh-Bénard convection without Boussinesq symmetry. Zbl 1051.76023 Mercader, Isabel; Prat, Joana; Knobloch, Edgar 13 2002 Normal forms for three-dimensional parametric instabilities in ideal hydrodynamics. Zbl 0814.76048 Knobloch, Edgar; Mahalov, Alex; Marsden, Jerrold E. 13 1994 Unfolding a tangent equilibrium-to-periodic heteroclinic cycle. Zbl 1187.34056 Champneys, Alan R.; Kirk, Vivien; Knobloch, Edgar; Oldeman, Bart E.; Rademacher, J. D. M. 12 2009 The diffusion of scalar and vector fields by homogeneous stationary turbulence. Zbl 0372.76042 Knobloch, Edgar 12 1977 Symmetry-breaking bifurcations on cubic lattices. Zbl 0909.58007 Callahan, T. K.; Knobloch, E. 11 1997 Long-wave Marangoni instability with vibration. Zbl 1097.76028 Thiele, Uwe; Vega, José M.; Knobloch, Edgar 11 2006 Classification of spatially localized oscillations in periodically forced dissipative systems. Zbl 1168.35003 Burke, J.; Yochelis, A.; Knobloch, E. 11 2008 Subcritical turbulent condensate in rapidly rotating Rayleigh-Bénard convection. Zbl 1415.76269 Favier, Benjamin; Guervilly, Céline; Knobloch, Edgar 11 2019 Pattern selection in ferrofluids. Zbl 0639.76055 Silber, Mary; Knobloch, Edgar 10 1988 Bifurcations in a model of magnetoconvection. Zbl 0583.76057 Knobloch, E.; Weiss, N. O. 10 1983 A stochastic return map for stochastic differential equations. Zbl 0714.60044 Weiss, Jeffrey B.; Knobloch, Edgar 10 1990 An unfolding of the Takens-Bogdanov singularity. Zbl 0731.58049 Hirschberg, P.; Knobloch, E. 10 1991 Heteroclinic bifurcations in a simple model of double-diffusive convection. Zbl 0770.76061 Knobloch, E.; Proctor, M. R. E.; Weiss, N. O. 10 1992 Fully nonlinear oscillatory convection in a rotating layer. Zbl 1185.76594 Julien, Keith; Knobloch, Edgar 9 1997 Bursts in oscillatory systems with broken \(D_4\) symmetry. Zbl 0941.34024 Moehlis, Jeff; Knobloch, Edgar 9 2000 Stability of spiral chimera states on a torus. Zbl 1386.37047 Omel’chenko, Oleh E.; Wolfrum, Matthias; Knobloch, Edgar 9 2018 Doubly diffusive waves. Zbl 0602.76092 Knobloch, Edgar; Deane, Anil E.; Toomre, Juri; Moore, Daniel R. 9 1986 Bifurcations in rotating systems. Zbl 0861.76089 Knobloch, E. 9 1994 On degenerate Hopf bifurcation with broken O(2) symmetry. Zbl 0671.34040 Crawford, John David; Knobloch, Edgar 8 1988 Strongly nonlinear magnetoconvection in three dimensions. Zbl 0944.76095 Julien, Keith; Knobloch, Edgar; Tobias, Steve 8 1999 Multipulse states in the Swift-Hohenberg equation. Zbl 1184.70019 Burke, J.; Knobloch, Edgar 8 2009 Oscillatory convection in a rotating layer. Zbl 0769.34029 Knobloch, E.; Silber, M. 8 1993 Magnetohydrodynamic convectons. Zbl 1241.76454 Lo Jacono, David; Bergeon, Alain; Knobloch, Edgar 8 2011 Transonic canards and stellar wind. Zbl 1377.34075 Carter, Paul; Knobloch, Edgar; Wechselberger, Martin 8 2017 Spatially localized structures in the Gray-Scott model. Zbl 1425.35099 Gandhi, Punit; Zelnik, Yuval R.; Knobloch, Edgar 8 2018 Impact of domain anisotropy on the inverse cascade in geostrophic turbulent convection. Zbl 1419.76586 Julien, Keith; Knobloch, Edgar; Plumley, Meredith 8 2018 Periodic and localized states in natural doubly diffusive convection. Zbl 1138.76039 Bergeon, A.; Knobloch, E. 7 2008 Nonlinear magnetoconvection in the presence of strong oblique fields. Zbl 1043.76022 Julien, K.; Knobloch, E.; Tobias, S. M. 7 2000 Complex dynamics in the 1:3 spatial resonance. Zbl 0980.34034 Porter, J.; Knobloch, E. 7 2000 Mode interactions in large aspect ratio convection. Zbl 0902.76035 Hirschberg, P.; Knobloch, E. 7 1997 Normal form for spatial dynamics in the Swift-Hohenberg equation. Zbl 1163.37394 Burke, John; Knobloch, Edgar 7 2007 A new resonance mechanism in the Swift-Hohenberg equation with time-periodic forcing. Zbl 1316.35030 Gandhi, Punit; Beaume, Cédric; Knobloch, Edgar 7 2015 Dynamics of counterpropagating waves in parametrically driven systems: dispersion vs. advection. Zbl 1076.35543 Martel, Carlos; Vega, José M.; Knobloch, Edgar 7 2003 Convectons in a rotating fluid layer. Zbl 1284.76139 Beaume, Cédric; Bergeon, Alain; Kao, Hsien-Ching; Knobloch, Edgar 7 2013 Classification and unifolding of degenerate Hopf bifurcations with 0(2) symmetry: No distinguished parameter. Zbl 0649.34050 Crawford, John David; Knobloch, Edgar 6 1988 Bursting mechanisms for hydrodynamical systems. Zbl 0981.76035 Knobloch, E.; Moehlis, J. 6 1999 Nonlinear doubly diffusive convection in vertical enclosures. Zbl 0945.35072 Bardan, G.; Bergeon, A.; Knobloch, E.; Mojtabi, A. 6 2000 Three-dimensional Marangoni-Bénard flows in square and nearly square containers. Zbl 1184.76050 Bergeon, A.; Henry, D.; Knobloch, E. 6 2001 Heteroclinic dynamics in the nonlocal parametrically driven nonlinear Schrödinger equation. Zbl 0988.35155 Higuera, M.; Porter, J.; Knobloch, E. 6 2002 Long dynamo waves. Zbl 1089.35062 Mason, Joanne; Knobloch, Edgar 6 2005 Dynamics in the 1:2 spatial resonance with broken reflection symmetry. Zbl 1082.37054 Porter, J.; Knobloch, E. 6 2005 Hopf bifurcation with \(Z_ 4 \times{}T^ 2\) symmetry. Zbl 0767.34023 Knobloch, E.; Silber, M. 6 1992 Three-dimensional spatially localized binary-fluid convection in a porous medium. Zbl 1291.76295 Lo Jacono, David; Bergeon, Alain; Knobloch, Edgar 6 2013 Coupled amplitude-streaming flow equations for nearly inviscid Faraday waves in small aspect ratio containers. Zbl 1084.76510 Higuera, M.; Vega, J. M.; Knobloch, E. 6 2002 The long-wave instability of a defect in a uniform parallel shear. Zbl 0642.76059 Lerner, J.; Knobloch, E. 5 1988 Complex dynamics in the Hopf bifurcation with broken translation symmetry. Zbl 0891.34044 Hirschberg, P.; Knobloch, E. 5 1996 Transient spatio-temporal chaos in the complex Ginzburg-Landau equation on long domains. Zbl 1236.35178 Houghton, S. M.; Knobloch, E.; Tobias, S. M.; Proctor, M. R. E. 5 2010 Mode interaction in rotating Rayleigh–Bénard convection. Zbl 1060.76549 Rüdiger, Sten; Knobloch, Edgar 5 2003 Staircase solutions and stability in vertically confined salt-finger convection. Zbl 1526.76019 Liu, Chang; Julien, Keith; Knobloch, Edgar 1 2022 Origin, bifurcation structure and stability of localized states in Kerr dispersive optical cavities. Zbl 1479.78019 Parra-Rivas, P.; Knobloch, E.; Gelens, L.; Gomila, D. 3 2021 Snaking without subcriticality: grain boundaries as non-topological defects. Zbl 07452524 Subramanian, Priya; Archer, Andrew J.; Knobloch, Edgar; Rucklidge, Alastair M. 3 2021 Stationary peaks in a multivariable reaction-diffusion system : foliated snaking due to subcritical Turing instability. Zbl 1480.92095 Knobloch, Edgar; Yochelis, Arik 1 2021 Curvature effects and radial homoclinic snaking. Zbl 07452521 Gomila, Damià; Knobloch, Edgar 1 2021 Robust wall states in rapidly rotating Rayleigh-Bénard convection. Zbl 1460.76719 Favier, Benjamin; Knobloch, Edgar 14 2020 Subcritical turbulent condensate in rapidly rotating Rayleigh-Bénard convection. Zbl 1415.76269 Favier, Benjamin; Guervilly, Céline; Knobloch, Edgar 11 2019 Jet formation in salt-finger convection: a modified Rayleigh-Bénard problem. Zbl 1415.76199 Xie, Jin-Han; Julien, Keith; Knobloch, Edgar 2 2019 Three-dimensional doubly diffusive convectons: instability and transition to complex dynamics. Zbl 1419.76214 Beaume, Cédric; Bergeon, Alain; Knobloch, Edgar 14 2018 Stability of spiral chimera states on a torus. Zbl 1386.37047 Omel’chenko, Oleh E.; Wolfrum, Matthias; Knobloch, Edgar 9 2018 Spatially localized structures in the Gray-Scott model. Zbl 1425.35099 Gandhi, Punit; Zelnik, Yuval R.; Knobloch, Edgar 8 2018 Impact of domain anisotropy on the inverse cascade in geostrophic turbulent convection. Zbl 1419.76586 Julien, Keith; Knobloch, Edgar; Plumley, Meredith 8 2018 Transonic canards and stellar wind. Zbl 1377.34075 Carter, Paul; Knobloch, Edgar; Wechselberger, Martin 8 2017 Chaos in the Takens-Bogdanov bifurcation with \(\mathrm{O}(2)\) symmetry. Zbl 1457.37069 Rucklidge, A. M.; Knobloch, E. 4 2017 Stability on time-dependent domains: convective and dilution effects. Zbl 1378.35030 Krechetnikov, R.; Knobloch, E. 3 2017 Ducks in space: from nonlinear absolute instability to noise-sustained structures in a pattern-forming system. Zbl 1404.35249 Avitabile, D.; Desroches, M.; Knobloch, E.; Krupa, M. 2 2017 A nonlinear model for rotationally constrained convection with Ekman pumping. Zbl 1422.76165 Julien, Keith; Aurnou, Jonathan M.; Calkins, Michael A.; Knobloch, Edgar; Marti, Philippe; Stellmach, Stephan; Vasil, Geoffrey M. 15 2016 Localized structures and front propagation in systems with a conservation law. Zbl 1404.35037 Knobloch, E. 3 2016 Two-dimensional localized structures in harmonically forced oscillatory systems. Zbl 1376.35095 Ma, Y.-P.; Knobloch, E. 2 2016 Problems on time-varying domains: formulation, dynamics, and challenges. Zbl 1332.35004 Knobloch, E.; Krechetnikov, R. 30 2015 A new resonance mechanism in the Swift-Hohenberg equation with time-periodic forcing. Zbl 1316.35030 Gandhi, Punit; Beaume, Cédric; Knobloch, Edgar 7 2015 Dynamic patterns in the reduced Craik-Leibovich equations. Zbl 1326.76084 Zhang, Zhexuan; Chini, Gregory P.; Julien, Keith; Knobloch, Edgar 3 2015 Stability on time-dependent domains. Zbl 1302.70057 Knobloch, E.; Krechetnikov, R. 5 2014 Convectons in a rotating fluid layer. Zbl 1284.76139 Beaume, Cédric; Bergeon, Alain; Kao, Hsien-Ching; Knobloch, Edgar 7 2013 Three-dimensional spatially localized binary-fluid convection in a porous medium. Zbl 1291.76295 Lo Jacono, David; Bergeon, Alain; Knobloch, Edgar 6 2013 Travelling convectons in binary fluid convection. Zbl 1287.76105 Mercader, Isabel; Batiste, Oriol; Alonso, Arantxa; Knobloch, Edgar 4 2013 Instabilities and dynamics of weakly subcritical patterns. Zbl 1294.35151 Kao, H.-C; Knobloch, E. 2 2013 Statistical and physical balances in low Rossby number Rayleigh-Bénard convection. Zbl 07649676 Julien, K.; Rubio, A. M.; Grooms, I.; Knobloch, E. 32 2012 Depinning, front motion, and phase slips. Zbl 1319.35251 Ma, Y.-P.; Knobloch, E. 4 2012 Spatially localized magnetoconvection. Zbl 1309.76221 Lo Jacono, D.; Bergeon, A.; Knobloch, E. 3 2012 Homoclinic snakes bounded by a saddle-center periodic orbit. Zbl 1260.34082 Champneys, A. R.; Knobloch, E.; Ma, Y.-P.; Wagenknecht, T. 3 2012 Convectons, anticonvectons and multiconvectons in binary fluid convection. Zbl 1225.76107 Mercader, Isabel; Batiste, Oriol; Alonso, Arantxa; Knobloch, Edgar 14 2011 Magnetohydrodynamic convectons. Zbl 1241.76454 Lo Jacono, David; Bergeon, Alain; Knobloch, Edgar 8 2011 To snake or not to snake in the planar Swift-Hohenberg equation. Zbl 1200.37014 Avitabile, Daniele; Lloyd, David J. B.; Burke, John; Knobloch, Edgar; Sandstede, Björn 39 2010 Defect-mediated snaking: a new growth mechanism for localized structures. Zbl 1213.37033 Ma, Y.-P.; Burke, J.; Knobloch, E. 15 2010 Transient spatio-temporal chaos in the complex Ginzburg-Landau equation on long domains. Zbl 1236.35178 Houghton, S. M.; Knobloch, E.; Tobias, S. M.; Proctor, M. R. E. 5 2010 Magnetorotational instability: recent developments. Zbl 1192.76068 Julien, Keith; Knobloch, Edgar 5 2010 Convectons in periodic and bounded domains. Zbl 1423.76125 Mercader, Isabel; Batiste, Oriol; Alonso, Arantxa; Knobloch, Edgar 4 2010 Spatially localized binary fluid convection in a porous medium. Zbl 1190.76077 Lo Jacono, D.; Bergeon, A.; Knobloch, E. 4 2010 Unfolding a tangent equilibrium-to-periodic heteroclinic cycle. Zbl 1187.34056 Champneys, Alan R.; Kirk, Vivien; Knobloch, Edgar; Oldeman, Bart E.; Rademacher, J. D. M. 12 2009 Multipulse states in the Swift-Hohenberg equation. Zbl 1184.70019 Burke, J.; Knobloch, Edgar 8 2009 Heteroclinic dynamics in a model of Faraday waves in a square container. Zbl 1181.37089 Moehlis, Jeff; Porter, Jeff; Knobloch, Edgar 2 2009 An asymptotically reduced model of turbulent Langmuir circulation. Zbl 1515.86004 Chini, Gregory P.; Julien, Keith; Knobloch, Edgar 2 2009 Bistability in the complex Ginzburg-Landau equation with drift. Zbl 1173.35352 Houghton, S. M.; Tobias, S. M.; Knobloch, E.; Proctor, M. R. E. 1 2009 Spatially localized structures in dissipative systems: open problems. Zbl 1139.35002 Knobloch, E. 37 2008 Spatially localized states in natural doubly diffusive convection. Zbl 1182.76055 Bergeon, A.; Knobloch, E. 13 2008 Classification of spatially localized oscillations in periodically forced dissipative systems. Zbl 1168.35003 Burke, J.; Yochelis, A.; Knobloch, E. 11 2008 Periodic and localized states in natural doubly diffusive convection. Zbl 1138.76039 Bergeon, A.; Knobloch, E. 7 2008 Spatially localized states in Marangoni convection in binary mixtures. Zbl 1148.76024 Assemat, P.; Bergeon, A.; Knobloch, E. 4 2008 Homoclinic snaking: Structure and stability. Zbl 1163.37317 Burke, John; Knobloch, Edgar 66 2007 When Shil’nikov meets Hopf in excitable systems. Zbl 1170.34025 Champneys, Alan R.; Kirk, Vivien; Knobloch, Edgar; Oldeman, Bart E.; Sneyd, James 27 2007 Reduced models for fluid flows with strong constraints. Zbl 1144.81362 Julien, Keith; Knobloch, Edgar 26 2007 Normal form for spatial dynamics in the Swift-Hohenberg equation. Zbl 1163.37394 Burke, John; Knobloch, Edgar 7 2007 Nonlinear Marangoni convection in circular and elliptical cylinders. Zbl 1182.76034 Assemat, P.; Bergeon, A.; Knobloch, E. 3 2007 Snakes and ladders: localized states in the Swift-Hohenberg equation. Zbl 1236.35144 Burke, John; Knobloch, Edgar 78 2006 Numerical simulation of an asymptotically reduced system for rotationally constrained convection. Zbl 1119.76057 Sprague, Michael; Julien, Keith; Knobloch, Edgar; Werne, Joseph 48 2006 Spatially localized binary-fluid convection. Zbl 1122.76029 Batiste, Oriol; Knobloch, Edgar; Alonso, Arantxa; Mercader, Isabel 35 2006 Generalized quasi-geostrophy for spatially anisotropic rotationally constrained flows. Zbl 1090.76077 Julien, Keith; Knobloch, Edgar; Milliff, Ralph; Werne, Joseph 26 2006 Long-wave Marangoni instability with vibration. Zbl 1097.76028 Thiele, Uwe; Vega, José M.; Knobloch, Edgar 11 2006 Long dynamo waves. Zbl 1089.35062 Mason, Joanne; Knobloch, Edgar 6 2005 Dynamics in the 1:2 spatial resonance with broken reflection symmetry. Zbl 1082.37054 Porter, J.; Knobloch, E. 6 2005 Dynamics of nearly inviscid Faraday waves in almost circular containers. Zbl 1143.76428 Higuera, M.; Knobloch, E.; Vega, J. M. 5 2005 Saturation of the magnetorotational instability. Zbl 1187.76278 Knobloch, Edgar; Julien, Keith 3 2005 Simulations of oscillatory convection in \({}^3\text{He}--{}^4\text{He}\) mixtures in moderate aspect ratio containers. Zbl 1187.76039 Batiste, Oriol; Knobloch, Edgar 2 2005 Thin liquid films on a slightly inclined heated plate. Zbl 1063.76032 Thiele, Uwe; Knobloch, Edgar 41 2004 Front and back instability of a liquid film on a slightly inclined plate. Zbl 1186.76522 Thiele, Uwe; Knobloch, Edgar 17 2003 Dynamics of counterpropagating waves in parametrically driven systems: dispersion vs. advection. Zbl 1076.35543 Martel, Carlos; Vega, José M.; Knobloch, Edgar 7 2003 Mode interaction in rotating Rayleigh–Bénard convection. Zbl 1060.76549 Rüdiger, Sten; Knobloch, Edgar 5 2003 Oscillatory marangoni convection in binary mixtures in square and nearly square containers. Zbl 1186.76054 Bergeon, A.; Knobloch, E. 3 2003 Oscillatory binary fluid convection in finite containers. Zbl 1132.92345 Batiste, Oriol; Knobloch, Edgar 1 2003 Highly supercritical convection in strong magnetic fields. Zbl 1099.85006 Julien, Keith; Knobloch, Edgar; Tobias, Steve 1 2003 Natural doubly diffusive convection in three-dimensional enclosures. Zbl 1185.76049 Bergeon, A.; Knobloch, E. 13 2002 Robust heteroclinic cycles in two-dimensional Rayleigh-Bénard convection without Boussinesq symmetry. Zbl 1051.76023 Mercader, Isabel; Prat, Joana; Knobloch, Edgar 13 2002 Heteroclinic dynamics in the nonlocal parametrically driven nonlinear Schrödinger equation. Zbl 0988.35155 Higuera, M.; Porter, J.; Knobloch, E. 6 2002 Coupled amplitude-streaming flow equations for nearly inviscid Faraday waves in small aspect ratio containers. Zbl 1084.76510 Higuera, M.; Vega, J. M.; Knobloch, E. 6 2002 The 1:2 mode interaction in Rayleigh-Bénard convection with and without Boussinesq symmetry. Zbl 1051.76556 Prat, Joana; Mercader, Isabel; Knobloch, Edgar 5 2002 Nearly inviscid Faraday waves. Zbl 1006.76025 Knobloch, Edgar; Vega, José M. 1 2002 New type of complex dynamics in the \(1:2\) spatial resonance. Zbl 0979.70017 Porter, J.; Knobloch, E. 20 2001 Nearly inviscid Faraday waves in annular containers of moderately large aspect ratio. Zbl 1029.76017 Vega, José M.; Knobloch, Edgar; Martel, Carlos 14 2001 Three-dimensional Marangoni-Bénard flows in square and nearly square containers. Zbl 1184.76050 Bergeon, A.; Henry, D.; Knobloch, E. 6 2001 Wrinkled tori and bursts due to resonant temporal forcing. Zbl 1020.37030 Moehlis, Jeff; Knobloch, Edgar 1 2001 Interaction of nearly-inviscid, multi-mode Faraday waves and mean flows. Zbl 1056.76511 Higuera, María J.; Vega, José M.; Knobloch, Edgar 1 2001 Bifurctions, patterns and symmetry. Selected papers dedicated to the memory of John David Crawford. Zbl 0956.00057 118 2000 Dynamics of counterpropagating waves in parametrically forced systems. Zbl 0949.35019 Martel, Carlos; Knobloch, Edgar; Vega, José M. 18 2000 Target patterns and spirals in planar reaction-diffusion systems. Zbl 0965.35084 Golubitsky, M.; Knobloch, E.; Stewart, I. 13 2000 Bursts in oscillatory systems with broken \(D_4\) symmetry. Zbl 0941.34024 Moehlis, Jeff; Knobloch, Edgar 9 2000 Nonlinear magnetoconvection in the presence of strong oblique fields. Zbl 1043.76022 Julien, K.; Knobloch, E.; Tobias, S. M. 7 2000 Complex dynamics in the 1:3 spatial resonance. Zbl 0980.34034 Porter, J.; Knobloch, E. 7 2000 Nonlinear doubly diffusive convection in vertical enclosures. Zbl 0945.35072 Bardan, G.; Bergeon, A.; Knobloch, E.; Mojtabi, A. 6 2000 Noise-sustained structures due to convective instability in finite domains. Zbl 0963.35164 Proctor, M. R. E.; Tobias, S. M.; Knobloch, E. 4 2000 Burst mechanisms in hydrodynamics. Zbl 0995.76026 Knobloch, E.; Moehlis, J. 2 2000 Pattern formation in three-dimensional reaction-diffusion systems. Zbl 0935.35065 Callahan, T. K.; Knobloch, E. 35 1999 Fully nonlinear three-dimensional convection in a rapidly rotating layer. Zbl 1147.76426 Julien, Keith; Knobloch, Edgar 17 1999 Strongly nonlinear magnetoconvection in three dimensions. Zbl 0944.76095 Julien, Keith; Knobloch, Edgar; Tobias, Steve 8 1999 Bursting mechanisms for hydrodynamical systems. Zbl 0981.76035 Knobloch, E.; Moehlis, J. 6 1999 Convective and absolute instabilities of fluid flows in finite geometry. Zbl 0962.76526 Tobias, S. M.; Proctor, M. R. E.; Knobloch, E. 32 1998 A new class of equations for rotationally constrained flows. Zbl 0923.76338 Julien, Keith; Knobloch, Edgar; Werne, Joseph 27 1998 Strongly nonlinear convection cells in a rapidly rotating fluid layer: The tilted \(f\)-plane. Zbl 0922.76192 Julien, Keith; Knobloch, Edgar 19 1998 Rotating convection: recent developments. Zbl 1210.76077 Knobloch, Edgar 13 1998 A robust heteroclinic cycle in an \(O(2)\times Z_2\) steady-state mode interaction. Zbl 0897.58034 Hirschberg, P.; Knobloch, E. 5 1998 ...and 62 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,764 Authors 85 Knobloch, Edgar 29 Ha, Seung-Yeal 25 Julien, Keith A. 17 Nepomnyashchy, Alexander A. 15 Sandstede, Björn 15 Vega, José Manuel 13 Park, Hansol 13 Thiele, Uwe 12 Bergeon, Alain 12 Champneys, Alan R. 12 Tobias, Steven M. 11 Stewart, Ian Nicholas 10 Kühn, Christian 10 Lloyd, David J. B. 10 López, Juan Manuel 10 Miranville, Alain M. 9 Carter, Paul M. 9 Kunnen, Rudie P. J. 9 Marques, Francisco 9 Mercader, Isabel 9 Proctor, Michael Richard Edward 9 Rucklidge, Alastair M. 8 Aurnou, Jonathan M. 8 Calkins, Michael A. 8 Chomaz, Jean-Marc 8 Laing, Carlo R. 8 Oron, Alexander 8 Rademacher, Jens Diederich Michael 8 Scheel, Arnd 8 Zhang, Keke 7 Ahn, Hyunjin 7 Batiste, Oriol 7 Beaume, Cédric 7 Clercx, Herman J. H. 7 Golovin, Alexander A. 7 Golubitsky, Martin A. 7 Martel, Carlos 7 Moehlis, Jeff 7 Moroz, Irene M. 6 Al Saadi, Fahad 6 Alexakis, Alexandros 6 Alonso, Arantxa 6 Ashwin, Peter 6 Bramburger, Jason J. 6 Cherfils, Laurence 6 Clerc, Marcel G. 6 Dangelmayr, Gerhard 6 Dawes, Jonathan H. P. 6 Fakih, Hussein 6 Goh, Ryan N. 6 Kalliadasis, Serafim 6 Kirk, Vivien 6 Liao, Xinhao 6 Marsden, Jerrold Eldon 6 Meron, Ehud 6 Porter, Jeff 6 Renardy, Yuriko Yamamuro 6 Rodríguez-Luis, Alejandro J. 6 Schneider, Tobias M. 6 Silber, Mary 6 Van Kan, Adrian 6 Ward, Michael J. 5 Avitabile, Daniele 5 Chini, Gregory P. 5 Daviaud, François 5 Doelman, Arjen 5 Favier, Benjamin 5 Grooms, Ian G. 5 Herrero, Henar 5 Higuera, María J. 5 Holmes, Philip J. 5 Kim, Dohyun 5 Krauskopf, Bernd 5 Kurths, Jürgen 5 Lohse, Detlef 5 Marti, Philippe 5 Podvigina, Ol’ga Mikhaĭlovna 5 Rubio, Antonio M. 5 Shim, Woojoo 5 Shishkina, Ol’ga Andreevna 5 Sun, Chunyou 5 Uecker, Hannes 5 Vasil, Geoffrey M. 5 Weiss, Nigel O. 5 Yochelis, Arik 4 Abshagen, J. 4 Algaba, Antonio 4 Breña-Medina, Víctor F. 4 Cao, Chongsheng 4 Chiffaudel, Arnaud 4 Chossat, Pascal 4 Couairon, Arnaud 4 Eckhardt, Bruno 4 Gaeta, Giuseppe 4 Gallaire, François 4 Guckenheimer, John M. 4 Hazel, Andrew L. 4 Hirschberg, P. 4 Iima, Makoto 4 Kang, Myeongju ...and 1,664 more Authors all top 5 Cited in 175 Serials 181 Journal of Fluid Mechanics 149 Physica D 86 Chaos 73 Physics of Fluids 37 Geophysical and Astrophysical Fluid Dynamics 35 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 33 SIAM Journal on Applied Dynamical Systems 22 Nonlinearity 21 Journal of Nonlinear Science 19 Journal of Differential Equations 15 Journal of Mathematical Physics 15 Journal of Statistical Physics 15 European Journal of Mechanics. B. Fluids 15 Communications in Nonlinear Science and Numerical Simulation 14 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 12 Nonlinear Dynamics 11 Discrete and Continuous Dynamical Systems. Series B 10 Chaos, Solitons and Fractals 9 Applied Mathematics and Computation 8 Journal of Mathematical Analysis and Applications 8 ZAMP. Zeitschrift für angewandte Mathematik und Physik 8 Bulletin of Mathematical Biology 8 Journal of Dynamics and Differential Equations 8 Networks and Heterogeneous Media 7 Archive for Rational Mechanics and Analysis 7 Journal of Mathematical Biology 7 Theoretical and Computational Fluid Dynamics 7 Dynamical Systems 6 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 6 SIAM Journal on Mathematical Analysis 6 New Journal of Physics 6 Journal of Statistical Mechanics: Theory and Experiment 6 Journal of Physics A: Mathematical and Theoretical 5 Communications in Mathematical Physics 5 Fluid Dynamics 5 Journal of Computational Physics 5 Journal of Engineering Mathematics 5 Quarterly of Applied Mathematics 5 Studies in Applied Mathematics 5 Applied Mathematics Letters 5 Dynamics and Stability of Systems 5 Discrete and Continuous Dynamical Systems 5 Discrete and Continuous Dynamical Systems. Series S 5 Journal of Theoretical Biology 4 Computers and Fluids 4 Physics of Fluids, A 4 Meccanica 4 Acta Applicandae Mathematicae 4 Applied Mathematical Modelling 4 SIAM Journal on Applied Mathematics 4 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 4 Communications on Pure and Applied Analysis 4 Communications in Computational Physics 3 Acta Mechanica 3 Applicable Analysis 3 Physics Reports 3 Asymptotic Analysis 3 European Journal of Applied Mathematics 3 Abstract and Applied Analysis 3 Journal of Applied Mechanics and Technical Physics 3 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 3 Nonlinear Analysis. Real World Applications 2 International Journal of Modern Physics B 2 Computers & Mathematics with Applications 2 International Journal for Numerical Methods in Fluids 2 Journal of the Mechanics and Physics of Solids 2 Mathematical Biosciences 2 Physics Letters. A 2 Reviews of Modern Physics 2 Journal of Computational and Applied Mathematics 2 Journal of Pure and Applied Algebra 2 Mathematics and Computers in Simulation 2 Transactions of the American Mathematical Society 2 Bulletin of the Korean Mathematical Society 2 Applied Mathematics and Mechanics. (English Edition) 2 Mathematical and Computer Modelling 2 International Journal of Computer Mathematics 2 Journal of Non-Equilibrium Thermodynamics 2 Proceedings of the National Academy of Sciences of the United States of America 2 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2 Journal of Mathematical Sciences (New York) 2 Qualitative Theory of Dynamical Systems 2 Journal of Evolution Equations 2 Stochastics and Dynamics 2 Multiscale Modeling & Simulation 2 Mathematical Modelling of Natural Phenomena 2 Kinetic and Related Models 2 The Journal of Mathematical Neuroscience 2 Evolution Equations and Control Theory 2 Nonlinear Analysis. Theory, Methods & Applications 2 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 1 Astrophysics and Space Science 1 General Relativity and Gravitation 1 International Journal of Control 1 International Journal of Engineering Science 1 International Journal of Heat and Mass Transfer 1 International Journal of Theoretical Physics 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Journal of Applied Mathematics and Mechanics 1 Letters in Mathematical Physics ...and 75 more Serials all top 5 Cited in 42 Fields 514 Fluid mechanics (76-XX) 338 Partial differential equations (35-XX) 268 Dynamical systems and ergodic theory (37-XX) 252 Ordinary differential equations (34-XX) 136 Biology and other natural sciences (92-XX) 70 Numerical analysis (65-XX) 68 Classical thermodynamics, heat transfer (80-XX) 51 Statistical mechanics, structure of matter (82-XX) 39 Geophysics (86-XX) 37 Mechanics of particles and systems (70-XX) 31 Probability theory and stochastic processes (60-XX) 28 Astronomy and astrophysics (85-XX) 25 Mechanics of deformable solids (74-XX) 18 Systems theory; control (93-XX) 16 Global analysis, analysis on manifolds (58-XX) 13 Computer science (68-XX) 13 Quantum theory (81-XX) 12 Optics, electromagnetic theory (78-XX) 10 Operator theory (47-XX) 8 Combinatorics (05-XX) 8 Integral equations (45-XX) 7 Difference and functional equations (39-XX) 7 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 5 Information and communication theory, circuits (94-XX) 4 General and overarching topics; collections (00-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Differential geometry (53-XX) 2 Commutative algebra (13-XX) 2 Group theory and generalizations (20-XX) 2 Topological groups, Lie groups (22-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 1 Mathematical logic and foundations (03-XX) 1 Algebraic geometry (14-XX) 1 Nonassociative rings and algebras (17-XX) 1 Special functions (33-XX) 1 Functional analysis (46-XX) 1 Convex and discrete geometry (52-XX) 1 Algebraic topology (55-XX) 1 Statistics (62-XX) 1 Relativity and gravitational theory (83-XX) 1 Mathematics education (97-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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