Edit Profile (opens in new tab) Krauskopf, Bernd Compute Distance To: Compute Author ID: krauskopf.bernd Published as: Krauskopf, Bernd; Krauskopf, B. External Links: ORCID Documents Indexed: 134 Publications since 1993 5 Contributions as Editor Co-Authors: 85 Co-Authors with 131 Joint Publications 1,531 Co-Co-Authors all top 5 Co-Authors 8 single-authored 58 Osinga, Hinke Maria 9 Green, Kirk 9 Sieber, Jan 7 Hittmeyer, Stefanie 7 Lowenberg, Mark H. 7 Oldeman, Bart E. 7 Wilson, Richard Eddie 6 Doedel, Eusebius J. 5 Barton, David A. W. 5 Champneys, Alan R. 5 Desroches, Mathieu 5 Kriete, Hartje 5 Neild, Simon A. 4 England, J. P. 4 Erzgräber, Hartmut 4 Giraldo, Andrus 4 Keane, Andrew 4 Lenstra, Daan 4 Wieczorek, Sebastian M. 3 Aguirre, Pablo 3 Broderick, Neil G. R. 3 Engelborghs, Koen 3 Guckenheimer, John M. 3 Langfield, Peter 3 Postlethwaite, Claire M. 2 Coetzee, Etienne B. 2 Collins, Peter J. 2 Creaser, Jennifer L. 2 Hasan, Cris R. 2 Humphries, Antony R. 2 Kiss, Gabor 2 Lee, Clare M. 2 Mujica, José 2 Rousseau, Christiane 2 Shinohara, Katsutoshi 2 Thota, Phanikrishna 1 Broer, Henk W. 1 Calleja, Renato C. 1 Dellnitz, Michael 1 di Bernardo, Mario 1 Dijkstra, Henk A. 1 Domokos, Gábor 1 Fehér, Eszter 1 Galán-Vioque, Jorge 1 Hammerlindl, Andy 1 Hannam, James 1 Henderson, Michael E. 1 Hogan, John Wesley 1 Homburg, Ale Jan 1 Homer, Martin E. 1 Howcroft, Chris 1 Inagaki, Mizuho 1 Junge, Oliver 1 Khibnik, Alexander I. 1 Kirk, Vivien 1 Knowles, James A. C. 1 Kühn, Christian 1 Laing, Carlo R. 1 Marten, Frank 1 Mason, Gemma 1 Musoke, Elle 1 Orosz, Gábor 1 Otupiri, Robert 1 Peckham, Bruce B. 1 Purewal, A. S. 1 Rieß, Thorsten 1 Rottschäfer, Vivi 1 Rübel, Jan 1 Ruschel, Stefan 1 Samaey, Giovanni 1 Sandstede, Björn 1 Schilder, Frank 1 Sharma, Sanjiv 1 Simpson, Thomas B. 1 Słowiński, Piotr 1 Starke, Jens 1 Szalai, Róbert 1 Terkovics, N. 1 Terrien, Soizic 1 Tzanov, Vassil V. 1 Vegter, Gert 1 Vladimirsky, Alexander 1 Wechselberger, Martin 1 Wille, Emilio C. G. 1 Zhang, Wenjun all top 5 Serials 24 SIAM Journal on Applied Dynamical Systems 21 Nonlinearity 13 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 7 Journal of Computational Dynamics 5 Physica D 4 Chaos 4 Dynamical Systems 4 Discrete and Continuous Dynamical Systems. Series B 3 Journal of Computational Physics 3 Discrete and Continuous Dynamical Systems 3 Nonlinear Dynamics 2 Ergodic Theory and Dynamical Systems 2 Experimental Mathematics 2 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 2 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 1 The Mathematical Intelligencer 1 CWI Quarterly 1 SIAM Review 1 Journal of Dynamics and Differential Equations 1 Indagationes Mathematicae. New Series 1 Bulletin of the Belgian Mathematical Society - Simon Stevin 1 Journal of Difference Equations and Applications 1 Journal of Vibration and Control 1 Nieuw Archief voor Wiskunde. Vijfde Serie 1 Physical Review E. Third Series 1 Journal of Mathematics and the Arts 1 Discrete and Continuous Dynamical Systems. Series S 1 The Journal of Mathematical Neuroscience 1 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 1 Understanding Complex Systems 1 Transactions of Mathematics and its Applications all top 5 Fields 97 Dynamical systems and ergodic theory (37-XX) 73 Ordinary differential equations (34-XX) 33 Numerical analysis (65-XX) 16 Optics, electromagnetic theory (78-XX) 13 Mechanics of particles and systems (70-XX) 9 Systems theory; control (93-XX) 7 Biology and other natural sciences (92-XX) 6 Functions of a complex variable (30-XX) 5 General and overarching topics; collections (00-XX) 4 General topology (54-XX) 4 Global analysis, analysis on manifolds (58-XX) 3 Differential geometry (53-XX) 3 Geophysics (86-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Partial differential equations (35-XX) 2 Mechanics of deformable solids (74-XX) 2 Statistical mechanics, structure of matter (82-XX) 2 Operations research, mathematical programming (90-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Fluid mechanics (76-XX) 1 Quantum theory (81-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 110 Publications have been cited 1,298 times in 737 Documents Cited by ▼ Year ▼ Mixed-mode oscillations with multiple time scales. Zbl 1250.34001Desroches, Mathieu; Guckenheimer, John; Krauskopf, Bernd; Kuehn, Christian; Osinga, Hinke M.; Wechselberger, Martin 158 2012 A survey of methods for computing (un)stable manifolds of vector fields. Zbl 1086.34002Krauskopf, B.; Osinga, H. M.; Doedel, E. J.; Henderson, M. E.; Guckenheimer, J.; Vladimirsky, A.; Dellnitz, M.; Junge, O. 86 2005 Resonant homoclinic flip bifurcations. Zbl 0990.37038Homburg, Ale Jan; Krauskopf, Bernd 48 2000 Growing 1D and quasi-2D unstable manifolds of maps. Zbl 0915.65075Krauskopf, Bernd; Osinga, Hinke 41 1998 Two-dimensional global manifolds of vector fields. Zbl 0983.37110Krauskopf, Bernd; Osinga, Hinke 33 1999 Numerical unfoldings of codimension-three resonant homoclinic flip bifurcations. Zbl 0990.37039Oldeman, Bart E.; Krauskopf, Bernd; Champneys, Alan R. 33 2001 A Lin’s method approach to finding and continuing heteroclinic connections involving periodic orbits. Zbl 1163.34028Krauskopf, Bernd; Rieß, Thorsten 32 2008 Numerical continuation methods for dynamical systems. Path following and boundary value problems. Zbl 1117.65005 32 2007 Bifurcation analysis of an inverted pendulum with delayed feedback control near a triple-zero eigenvalue singularity. Zbl 1054.34121Sieber, Jan; Krauskopf, Bernd 32 2004 Computing one-dimensional stable manifolds and stable sets of planar maps without the inverse. Zbl 1059.37067England, J. P.; Krauskopf, B.; Osinga, H. M. 31 2004 Mixed-mode oscillations and slow manifolds in the self-coupled Fitzhugh-Nagumo system. Zbl 1306.34050Desroches, Mathieu; Krauskopf, Bernd; Osinga, Hinke M. 27 2008 The geometry of slow manifolds near a folded node. Zbl 1167.34365Desroches, M.; Krauskopf, B.; Osinga, H. M. 26 2008 Computing invariant manifolds via the continuation of orbit segments. Zbl 1126.65111Krauskopf, Bernd; Osinga, Hinke M. 26 2007 Global study of a family of cubic Liénard equations. Zbl 0920.58034Khibnik, Alexander I.; Krauskopf, Bernd; Rousseau, Christiane 26 1998 Global bifurcations of the Lorenz manifold. Zbl 1118.34042Doedel, Eusebius; Krauskopf, Bernd; Osinga, Hinke M. 25 2006 Bifurcations and multiple traffic jams in a car-following model with reaction-time delay. Zbl 1097.90015Orosz, Gábor; Krauskopf, Bernd; Wilson, R. Eddie 22 2005 Computing geodesic level sets on global (un)stable manifolds of vector fields. Zbl 1089.37014Krauskopf, Bernd; Osinga, Hinke M. 22 2003 Resonance phenomena in a scalar delay differential equation with two state-dependent delays. Zbl 1371.34115Calleja, R. C.; Humphries, A. R.; Krauskopf, B. 22 2017 Numerical continuation of canard orbits in slow-fast dynamical systems. Zbl 1191.34072Desroches, M.; Krauskopf, B.; Osinga, H. M. 20 2010 Collocation schemes for periodic solutions of neutral delay differential equations. Zbl 1108.65089Barton, David A. W.; Krauskopf, Bernd; Wilson, R. Eddie 17 2006 Globalizing two-dimensional unstable manifolds of maps. Zbl 0955.37016Krauskopf, Bernd; Osinga, Hinke 17 1998 Global invariant manifolds in the transition to preturbulence in the Lorenz system. Zbl 1246.37037Doedel, Eusebius J.; Krauskopf, Bernd; Osinga, Hinke M. 16 2011 Global organization of phase space in the transition to chaos in the Lorenz system. Zbl 1332.34083Doedel, Eusebius J.; Krauskopf, Bernd; Osinga, Hinke M. 14 2015 Computing unstable manifolds of periodic orbits in delay differential equations. Zbl 1017.65102Krauskopf, Bernd; Green, Kirk 14 2003 How to find a codimension-one heteroclinic cycle between two periodic orbits. Zbl 1246.34047Zhang, Wenjun; Krauskopf, Bernd; Kirk, Vivien 14 2012 Investigating the consequences of global bifurcations for two-dimensional invariant manifolds of vector fields. Zbl 1216.34035Aguirre, Pablo; Doedel, Eusebius J.; Krauskopf, Bernd; Osinga, Hinke M. 14 2011 Tangency bifurcations of global Poincaré maps. Zbl 1159.37313Lee, Clare M.; Collins, Pieter J.; Krauskopf, Bernd; Osinga, Hinke M. 13 2008 Bifurcation analysis of delay-induced resonances of the El-Niño southern oscillation. Zbl 1320.86004Krauskopf, Bernd; Sieber, Jan 12 2014 Death of period-doublings: Locating the homoclinic-doubling cascade. Zbl 1011.34036Oldeman, Bart E.; Krauskopf, Bernd; Champneys, Alan R. 12 2000 Codimension-three unfoldings of reflectionally symmetric planar vector fields. Zbl 0904.34025Krauskopf, Bernd; Rousseau, Christiane 12 1997 Extending the permissible control loop latency for the controlled inverted pendulum. Zbl 1079.34060Sieber, J.; Krauskopf, B. 12 2005 Homoclinic branch switching: a numerical implementation of Lin’s method. Zbl 1057.37073Oldeman, Bart E.; Champneys, Alan R.; Krauskopf, Bernd 11 2003 Global invariant manifolds near homoclinic orbits to a real saddle: (non)orientability and flip bifurcation. Zbl 1284.34069Aguirre, Pablo; Krauskopf, Bernd; Osinga, Hinke M. 11 2013 Bifurcations of global reinjection orbits near a saddle-node Hopf bifurcation. Zbl 1109.37042Krauskopf, Bernd; Oldeman, Bart E. 11 2006 The geometry of mixed-mode oscillations in the Olsen model for the peroxidase-oxidase reaction. Zbl 1187.37121Desroches, Mathieu; Krauskopf, Bernd; Osinga, Hinke M. 10 2009 Complex balancing motions of an inverted pendulum subject to delayed feedback control. Zbl 1070.34105Sieber, J.; Krauskopf, B. 9 2004 Computing one-dimensional global manifolds of Poincaré maps by continuation. Zbl 1090.37055England, J. P.; Krauskopf, B.; Osinga, H. M. 9 2005 Investigating torus bifurcations in the forced Van der Pol oscillator. Zbl 0987.37079Krauskopf, Bernd; Osinga, Hinke M. 9 2000 Bifurcation sequences at 1:4 resonance: An inventory. Zbl 0804.58041Krauskopf, Bernd 9 1994 Delayed feedback versus seasonal forcing: resonance phenomena in an El Niño Southern Oscillation model. Zbl 1320.37038Keane, Andrew; Krauskopf, Bernd; Postlethwaite, Claire 9 2015 Periodic solutions and their bifurcations in a nonsmooth second-order delay differential equation. Zbl 1121.34071Barton, David A. W.; Krauskopf, Bernd; Wilson, R. Eddie 8 2006 Compound laser modes of mutually delay-coupled lasers. Zbl 1097.78014Erzgräber, Hartmut; Krauskopf, Bernd; Lenstra, Daan 8 2006 Stability implications of delay distribution for first-order and second-order systems. Zbl 1202.34127Kiss, Gábor; Krauskopf, Bernd 8 2010 Bifurcations of \(n\)-homoclinic orbits in optically injected lasers. Zbl 1115.34045Wieczorek, Sebastian; Krauskopf, Bernd 8 2005 Tangencies between global invariant manifolds and slow manifolds near a singular Hopf bifurcation. Zbl 1393.37035Mujica, José; Krauskopf, Bernd; Osinga, Hinke M. 8 2018 Saddle slow manifolds and canard orbits in \(\mathbb{R}^{4}\) and application to the full Hodgkin-Huxley model. Zbl 1395.92038Hasan, Cris R.; Krauskopf, Bernd; Osinga, Hinke M. 8 2018 Control-based bifurcation analysis for experiments. Zbl 1170.70399Sieber, Jan; Krauskopf, Bernd 7 2008 \(\alpha\)-flips and T-points in the Lorenz system. Zbl 1347.37052Creaser, Jennifer L.; Krauskopf, Bernd; Osinga, Hinke M. 7 2015 Solving Winfree’s puzzle: the isochrons in the FitzHugh-Nagumo model. Zbl 1374.37032Langfield, Peter; Krauskopf, Bernd; Osinga, Hinke M. 7 2014 Invariant manifolds and global bifurcations. Zbl 1374.37076Guckenheimer, John; Krauskopf, Bernd; Osinga, Hinke M.; Sandstede, Björn 7 2015 Finding first foliation tangencies in the Lorenz system. Zbl 1381.37097Creaser, Jennifer L.; Krauskopf, Bernd; Osinga, Hinke M. 7 2017 Saddle invariant objects and their global manifolds in a neighborhood of a homoclinic flip bifurcation of case B. Zbl 1385.37028Giraldo, Andrus; Krauskopf, Bernd; Osinga, Hinke M. 7 2017 Hausdorff convergence of Julia sets. Zbl 0915.58085Krauskopf, Bernd; Kriete, Hartje 7 1999 Bistability and torus break-up in a semiconductor laser with phase-conjugate feedback. Zbl 1023.34064Green, Kirk; Krauskopf, Bernd; Engelborghs, Koen 7 2002 The Lorenz manifold as a collection of geodesic level sets. Zbl 1083.37019Krauskopf, Bernd; Osinga, Hinke M. 7 2004 A global bifurcation analysis of the subcritical Hopf normal form subject to Pyragas time-delayed feedback control. Zbl 1323.37034Purewal, A. S.; Postlethwaite, C. M.; Krauskopf, B. 7 2014 Interacting global invariant sets in a planar map model of wild chaos. Zbl 1304.37023Hittmeyer, Stefanie; Krauskopf, Bernd; Osinga, Hinke M. 7 2013 Global invariant manifolds near a Shilnikov homoclinic bifurcation. Zbl 1309.34077Aguirre, Pablo; Krauskopf, Bernd; Osinga, Hinke M. 7 2014 Interaction of torsion and lateral bending in aircraft nose landing gear shimmy. Zbl 1176.74091Thota, Phanikrishna; Krauskopf, Bernd; Lowenberg, Mark 6 2009 Computing two-dimensional global invariant manifolds in slow-fast systems. Zbl 1140.37365England, J. P.; Krauskopf, B.; Osinga, H. M. 6 2007 A two-parameter study of the locking region of a semiconductor laser subject to phase-conjugate feedback. Zbl 1088.37522Green, Kirk; Krauskopf, Bernd; Samaey, Giovanni 6 2003 Investigating irregular behavior in a model for the El Niño southern oscillation with positive and negative delayed feedback. Zbl 1351.37270Keane, Andrew; Krauskopf, Bernd; Postlethwaite, Claire 6 2016 Kernel convergence of hyperbolic components. Zbl 0893.32011Krauskopf, Bernd; Kriete, Hartje 5 1997 Mixed-mode oscillations and twin canard orbits in an autocatalytic chemical reaction. Zbl 1381.37107Hasan, Cris R.; Krauskopf, Bernd; Osinga, Hinke M. 5 2017 Forward-time and backward-time isochrons and their interactions. Zbl 1358.37047Langfield, Peter; Krauskopf, Bernd; Osinga, Hinke M. 5 2015 The bifurcation set for the \(1:4\) resonance problem. Zbl 0828.34027Krauskopf, Bernd 5 1994 Crocheting the Lorenz manifold. Zbl 1073.37036Osinga, Hinke M.; Krauskopf, Bernd 5 2004 Accumulating regions of winding periodic orbits in optically driven lasers. Zbl 1047.78502Krauskopf, Bernd; Wieczorek, Sebastian 5 2002 Explicit periodic solutions in a model of a relay controller with delay and forcing. Zbl 1094.34048Barton, David A. W.; Krauskopf, Bernd; Wilson, R. Eddie 5 2005 One-dimensional unstable eigenfunction and manifold computations in delay differential equations. Zbl 1052.65115Green, Kirk; Krauskopf, Bernd; Engelborghs, Koen 5 2004 Global quantitative predictions of complex laser dynamics. Zbl 1244.78008Wieczorek, Sebastian; Simpson, Thomas B.; Krauskopf, Bernd; Lenstra, Daan 5 2002 Existence of blenders in a Hénon-like family: geometric insights from invariant manifold computations. Zbl 1402.37027Hittmeyer, Stefanie; Krauskopf, Bernd; Osinga, Hinke M.; Shinohara, Katsutoshi 5 2018 A planar model system for the saddle-node Hopf bifurcation with global reinjection. Zbl 1061.37028Krauskopf, Bernd; Oldeman, Bart E. 4 2004 Convergence of Julia sets in the approximation of \(\lambda e^ z\) by \(\lambda[1+(z/d)]^ d\). Zbl 0872.30019Krauskopf, Bernd 4 1993 The ECM-backbone of the Lang-Kobayashi equations: a geometric picture. Zbl 1148.78331Rottschäfer, Vivi; Krauskopf, Bernd 4 2007 Homoclinic bifurcations in a neutral delay model of a transmission line oscillator. Zbl 1129.34049Barton, David A. W.; Krauskopf, Bernd; Wilson, R. Eddie 4 2007 Bifurcation analysis of a semiconductor laser with filtered optical feedback. Zbl 1210.15006Erzgräber, Hartmut; Krauskopf, Bernd; Lenstra, Daan 4 2007 Chenciner bubbles and torus break-up in a periodically forced delay differential equation. Zbl 1393.37094Keane, A.; Krauskopf, B. 4 2018 Bifurcations of stable sets in noninvertible planar maps. Zbl 1085.37036England, J. P.; Krauskopf, B.; Osinga, H. M. 4 2005 Cascades of global bifurcations and chaos near a homoclinic flip bifurcation: a case study. Zbl 1408.37087Giraldo, Andrus; Krauskopf, Bernd; Osinga, Hinke M. 4 2018 Numerical continuation and bifurcation analysis in aircraft design: an industrial perspective. Zbl 1353.93084Sharma, Sanjiv; Coetzee, Etienne B.; Lowenberg, Mark H.; Neild, Simon A.; Krauskopf, Bernd 4 2015 Nonlinear dynamics of torsional waves in a drill-string model with spatial extent. Zbl 1269.74114Barton, David A. W.; Krauskopf, Bernd; Wilson, R. Eddie 4 2010 Stabilizing effect of delay distribution for a class of second-order systems without instantaneous feedback. Zbl 1219.34094Kiss, Gábor; Krauskopf, Bernd 4 2011 Efficient computation of quasiperiodic oscillations in nonlinear systems with fast rotating parts. Zbl 1170.70353Schilder, Frank; Rübel, Jan; Starke, Jens; Osinga, Hinke M.; Krauskopf, Bernd; Inagaki, Mizuho 3 2008 Global analysis of dynamical systems. Festschrift dedicated to Floris Takens for his 60th birthday. Zbl 0971.00062 3 2001 Interactions of the Julia set with critical and (un)stable sets in an angle-doubling map on \(\mathbb{C}\backslash\{0\}\). Zbl 1314.37034Hittmeyer, Stefanie; Krauskopf, Bernd; Osinga, Hinke M. 3 2015 Chaos and wild chaos in Lorenz-type systems. Zbl 1318.37009Osinga, Hinke M.; Krauskopf, Bernd; Hittmeyer, Stefanie 3 2014 The effect of state dependence in a delay differential equation model for the El Niño southern oscillation. Zbl 1462.86008Keane, Andrew; Krauskopf, Bernd; Dijkstra, Henk A. 3 2019 From wild Lorenz-like to wild Rovella-like dynamics. Zbl 1357.37059Hittmeyer, Stefanie; Krauskopf, Bernd; Osinga, Hinke M. 3 2015 A note on non-converging Julia sets. Zbl 0885.30022Krauskopf, B.; Kriete, H. 2 1996 The extended parameter space of a model for 1:4 resonance. Zbl 0856.34046Krauskopf, Bernd 2 1995 Bifurcations at \(\infty\) in a model for \(1:4\) resonance. Zbl 0884.58076Krauskopf, Bernd 2 1997 From local to global one-dimensional unstable manifolds in delay differential equations. Zbl 1106.34333Krauskopf, B.; Green, K.; Engelborghs, K. 2 2005 Control-based continuation of periodic orbits with a time-delayed difference scheme. Zbl 1168.34040Sieber, J.; Krauskopf, B. 2 2007 Unfolding the cusp-cusp bifurcation of planar endomorphisms. Zbl 1210.37021Krauskopf, Bernd; Osinga, Hinke M.; Peckham, Bruce B. 2 2007 Strong resonances and Takens’s Utrecht preprint. Zbl 1193.37067Krauskopf, Bernd 2 2001 Nonlinear dynamics and chaos: Where do we go from here? Zbl 0996.00035 2 2003 Codimension-one tangency bifurcations of global Poincaré maps of four-dimensional vector fields. Zbl 1175.37057Krauskopf, Bernd; Lee, Clare M.; Osinga, Hinke M. 2 2009 Bifurcation analysis of frequency locking in a semiconductor laser with phase-conjugate feedback. Zbl 1046.37508Green, Kirk; Krauskopf, Bernd 2 2003 Influence of variable side-stay geometry on the shimmy dynamics of an aircraft dual-wheel main landing gear. Zbl 1282.70044Howcroft, Chris; Krauskopf, Bernd; Lowenberg, Mark H.; Neild, Simon A. 2 2013 A surface of heteroclinic connections between two saddle slow manifolds in the Olsen model. Zbl 1461.34072Musoke, Elle; Krauskopf, Bernd; Osinga, Hinke M. 1 2020 How to identify a hyperbolic set as a blender. Zbl 1457.37044Hittmeyer, Stefanie; Krauskopf, Bernd; Osinga, Hinke M.; Shinohara, Katsutoshi 1 2020 The effect of state dependence in a delay differential equation model for the El Niño southern oscillation. Zbl 1462.86008Keane, Andrew; Krauskopf, Bernd; Dijkstra, Henk A. 3 2019 Tangencies between global invariant manifolds and slow manifolds near a singular Hopf bifurcation. Zbl 1393.37035Mujica, José; Krauskopf, Bernd; Osinga, Hinke M. 8 2018 Saddle slow manifolds and canard orbits in \(\mathbb{R}^{4}\) and application to the full Hodgkin-Huxley model. Zbl 1395.92038Hasan, Cris R.; Krauskopf, Bernd; Osinga, Hinke M. 8 2018 Existence of blenders in a Hénon-like family: geometric insights from invariant manifold computations. Zbl 1402.37027Hittmeyer, Stefanie; Krauskopf, Bernd; Osinga, Hinke M.; Shinohara, Katsutoshi 5 2018 Chenciner bubbles and torus break-up in a periodically forced delay differential equation. Zbl 1393.37094Keane, A.; Krauskopf, B. 4 2018 Cascades of global bifurcations and chaos near a homoclinic flip bifurcation: a case study. Zbl 1408.37087Giraldo, Andrus; Krauskopf, Bernd; Osinga, Hinke M. 4 2018 Resonance phenomena in a scalar delay differential equation with two state-dependent delays. Zbl 1371.34115Calleja, R. C.; Humphries, A. R.; Krauskopf, B. 22 2017 Finding first foliation tangencies in the Lorenz system. Zbl 1381.37097Creaser, Jennifer L.; Krauskopf, Bernd; Osinga, Hinke M. 7 2017 Saddle invariant objects and their global manifolds in a neighborhood of a homoclinic flip bifurcation of case B. Zbl 1385.37028Giraldo, Andrus; Krauskopf, Bernd; Osinga, Hinke M. 7 2017 Mixed-mode oscillations and twin canard orbits in an autocatalytic chemical reaction. Zbl 1381.37107Hasan, Cris R.; Krauskopf, Bernd; Osinga, Hinke M. 5 2017 A Lin’s method approach for detecting all canard orbits arising from a folded node. Zbl 1397.34096Mujica, José; Krauskopf, Bernd; Osinga, Hinke M. 2 2017 Investigating irregular behavior in a model for the El Niño southern oscillation with positive and negative delayed feedback. Zbl 1351.37270Keane, Andrew; Krauskopf, Bernd; Postlethwaite, Claire 6 2016 Global organization of phase space in the transition to chaos in the Lorenz system. Zbl 1332.34083Doedel, Eusebius J.; Krauskopf, Bernd; Osinga, Hinke M. 14 2015 Delayed feedback versus seasonal forcing: resonance phenomena in an El Niño Southern Oscillation model. Zbl 1320.37038Keane, Andrew; Krauskopf, Bernd; Postlethwaite, Claire 9 2015 \(\alpha\)-flips and T-points in the Lorenz system. Zbl 1347.37052Creaser, Jennifer L.; Krauskopf, Bernd; Osinga, Hinke M. 7 2015 Invariant manifolds and global bifurcations. Zbl 1374.37076Guckenheimer, John; Krauskopf, Bernd; Osinga, Hinke M.; Sandstede, Björn 7 2015 Forward-time and backward-time isochrons and their interactions. Zbl 1358.37047Langfield, Peter; Krauskopf, Bernd; Osinga, Hinke M. 5 2015 Numerical continuation and bifurcation analysis in aircraft design: an industrial perspective. Zbl 1353.93084Sharma, Sanjiv; Coetzee, Etienne B.; Lowenberg, Mark H.; Neild, Simon A.; Krauskopf, Bernd 4 2015 Interactions of the Julia set with critical and (un)stable sets in an angle-doubling map on \(\mathbb{C}\backslash\{0\}\). Zbl 1314.37034Hittmeyer, Stefanie; Krauskopf, Bernd; Osinga, Hinke M. 3 2015 From wild Lorenz-like to wild Rovella-like dynamics. Zbl 1357.37059Hittmeyer, Stefanie; Krauskopf, Bernd; Osinga, Hinke M. 3 2015 Mode structure of a semiconductor laser with feedback from two external filters. Zbl 1330.78018Słowiński, Piotr; Krauskopf, Bernd; Wieczorek, Sebastian 1 2015 Bifurcation analysis of delay-induced resonances of the El-Niño southern oscillation. Zbl 1320.86004Krauskopf, Bernd; Sieber, Jan 12 2014 Solving Winfree’s puzzle: the isochrons in the FitzHugh-Nagumo model. Zbl 1374.37032Langfield, Peter; Krauskopf, Bernd; Osinga, Hinke M. 7 2014 A global bifurcation analysis of the subcritical Hopf normal form subject to Pyragas time-delayed feedback control. Zbl 1323.37034Purewal, A. S.; Postlethwaite, C. M.; Krauskopf, B. 7 2014 Global invariant manifolds near a Shilnikov homoclinic bifurcation. Zbl 1309.34077Aguirre, Pablo; Krauskopf, Bernd; Osinga, Hinke M. 7 2014 Chaos and wild chaos in Lorenz-type systems. Zbl 1318.37009Osinga, Hinke M.; Krauskopf, Bernd; Hittmeyer, Stefanie 3 2014 Global invariant manifolds near homoclinic orbits to a real saddle: (non)orientability and flip bifurcation. Zbl 1284.34069Aguirre, Pablo; Krauskopf, Bernd; Osinga, Hinke M. 11 2013 Interacting global invariant sets in a planar map model of wild chaos. Zbl 1304.37023Hittmeyer, Stefanie; Krauskopf, Bernd; Osinga, Hinke M. 7 2013 Influence of variable side-stay geometry on the shimmy dynamics of an aircraft dual-wheel main landing gear. Zbl 1282.70044Howcroft, Chris; Krauskopf, Bernd; Lowenberg, Mark H.; Neild, Simon A. 2 2013 Mixed-mode oscillations with multiple time scales. Zbl 1250.34001Desroches, Mathieu; Guckenheimer, John; Krauskopf, Bernd; Kuehn, Christian; Osinga, Hinke M.; Wechselberger, Martin 158 2012 How to find a codimension-one heteroclinic cycle between two periodic orbits. Zbl 1246.34047Zhang, Wenjun; Krauskopf, Bernd; Kirk, Vivien 14 2012 Global invariant manifolds in the transition to preturbulence in the Lorenz system. Zbl 1246.37037Doedel, Eusebius J.; Krauskopf, Bernd; Osinga, Hinke M. 16 2011 Investigating the consequences of global bifurcations for two-dimensional invariant manifolds of vector fields. Zbl 1216.34035Aguirre, Pablo; Doedel, Eusebius J.; Krauskopf, Bernd; Osinga, Hinke M. 14 2011 Stabilizing effect of delay distribution for a class of second-order systems without instantaneous feedback. Zbl 1219.34094Kiss, Gábor; Krauskopf, Bernd 4 2011 Numerical continuation of canard orbits in slow-fast dynamical systems. Zbl 1191.34072Desroches, M.; Krauskopf, B.; Osinga, H. M. 20 2010 Stability implications of delay distribution for first-order and second-order systems. Zbl 1202.34127Kiss, Gábor; Krauskopf, Bernd 8 2010 Nonlinear dynamics of torsional waves in a drill-string model with spatial extent. Zbl 1269.74114Barton, David A. W.; Krauskopf, Bernd; Wilson, R. Eddie 4 2010 The geometry of mixed-mode oscillations in the Olsen model for the peroxidase-oxidase reaction. Zbl 1187.37121Desroches, Mathieu; Krauskopf, Bernd; Osinga, Hinke M. 10 2009 Interaction of torsion and lateral bending in aircraft nose landing gear shimmy. Zbl 1176.74091Thota, Phanikrishna; Krauskopf, Bernd; Lowenberg, Mark 6 2009 Codimension-one tangency bifurcations of global Poincaré maps of four-dimensional vector fields. Zbl 1175.37057Krauskopf, Bernd; Lee, Clare M.; Osinga, Hinke M. 2 2009 Amplitude-phase dynamics near the locking region of two delay-coupled semiconductor lasers. Zbl 1165.37037Erzgräber, H.; Wille, E.; Krauskopf, B.; Fischer, I. 1 2009 Bifurcation analysis of a spatially extended laser with optical feedback. Zbl 1167.37047Green, Kirk; Krauskopf, Bernd; Marten, Frank; Lenstra, Daan 1 2009 A Lin’s method approach to finding and continuing heteroclinic connections involving periodic orbits. Zbl 1163.34028Krauskopf, Bernd; Rieß, Thorsten 32 2008 Mixed-mode oscillations and slow manifolds in the self-coupled Fitzhugh-Nagumo system. Zbl 1306.34050Desroches, Mathieu; Krauskopf, Bernd; Osinga, Hinke M. 27 2008 The geometry of slow manifolds near a folded node. Zbl 1167.34365Desroches, M.; Krauskopf, B.; Osinga, H. M. 26 2008 Tangency bifurcations of global Poincaré maps. Zbl 1159.37313Lee, Clare M.; Collins, Pieter J.; Krauskopf, Bernd; Osinga, Hinke M. 13 2008 Control-based bifurcation analysis for experiments. Zbl 1170.70399Sieber, Jan; Krauskopf, Bernd 7 2008 Efficient computation of quasiperiodic oscillations in nonlinear systems with fast rotating parts. Zbl 1170.70353Schilder, Frank; Rübel, Jan; Starke, Jens; Osinga, Hinke M.; Krauskopf, Bernd; Inagaki, Mizuho 3 2008 Numerical continuation methods for dynamical systems. Path following and boundary value problems. Zbl 1117.65005 32 2007 Computing invariant manifolds via the continuation of orbit segments. Zbl 1126.65111Krauskopf, Bernd; Osinga, Hinke M. 26 2007 Computing two-dimensional global invariant manifolds in slow-fast systems. Zbl 1140.37365England, J. P.; Krauskopf, B.; Osinga, H. M. 6 2007 The ECM-backbone of the Lang-Kobayashi equations: a geometric picture. Zbl 1148.78331Rottschäfer, Vivi; Krauskopf, Bernd 4 2007 Homoclinic bifurcations in a neutral delay model of a transmission line oscillator. Zbl 1129.34049Barton, David A. W.; Krauskopf, Bernd; Wilson, R. Eddie 4 2007 Bifurcation analysis of a semiconductor laser with filtered optical feedback. Zbl 1210.15006Erzgräber, Hartmut; Krauskopf, Bernd; Lenstra, Daan 4 2007 Control-based continuation of periodic orbits with a time-delayed difference scheme. Zbl 1168.34040Sieber, J.; Krauskopf, B. 2 2007 Unfolding the cusp-cusp bifurcation of planar endomorphisms. Zbl 1210.37021Krauskopf, Bernd; Osinga, Hinke M.; Peckham, Bruce B. 2 2007 Visualizing curvature on the Lorenz manifold. Zbl 1122.53001Osinga, H. M.; Krauskopf, B. 1 2007 Global bifurcations of the Lorenz manifold. Zbl 1118.34042Doedel, Eusebius; Krauskopf, Bernd; Osinga, Hinke M. 25 2006 Collocation schemes for periodic solutions of neutral delay differential equations. Zbl 1108.65089Barton, David A. W.; Krauskopf, Bernd; Wilson, R. Eddie 17 2006 Bifurcations of global reinjection orbits near a saddle-node Hopf bifurcation. Zbl 1109.37042Krauskopf, Bernd; Oldeman, Bart E. 11 2006 Periodic solutions and their bifurcations in a nonsmooth second-order delay differential equation. Zbl 1121.34071Barton, David A. W.; Krauskopf, Bernd; Wilson, R. Eddie 8 2006 Compound laser modes of mutually delay-coupled lasers. Zbl 1097.78014Erzgräber, Hartmut; Krauskopf, Bernd; Lenstra, Daan 8 2006 A survey of methods for computing (un)stable manifolds of vector fields. Zbl 1086.34002Krauskopf, B.; Osinga, H. M.; Doedel, E. J.; Henderson, M. E.; Guckenheimer, J.; Vladimirsky, A.; Dellnitz, M.; Junge, O. 86 2005 Bifurcations and multiple traffic jams in a car-following model with reaction-time delay. Zbl 1097.90015Orosz, Gábor; Krauskopf, Bernd; Wilson, R. Eddie 22 2005 Extending the permissible control loop latency for the controlled inverted pendulum. Zbl 1079.34060Sieber, J.; Krauskopf, B. 12 2005 Computing one-dimensional global manifolds of Poincaré maps by continuation. Zbl 1090.37055England, J. P.; Krauskopf, B.; Osinga, H. M. 9 2005 Bifurcations of \(n\)-homoclinic orbits in optically injected lasers. Zbl 1115.34045Wieczorek, Sebastian; Krauskopf, Bernd 8 2005 Explicit periodic solutions in a model of a relay controller with delay and forcing. Zbl 1094.34048Barton, David A. W.; Krauskopf, Bernd; Wilson, R. Eddie 5 2005 Bifurcations of stable sets in noninvertible planar maps. Zbl 1085.37036England, J. P.; Krauskopf, B.; Osinga, H. M. 4 2005 From local to global one-dimensional unstable manifolds in delay differential equations. Zbl 1106.34333Krauskopf, B.; Green, K.; Engelborghs, K. 2 2005 Chaotic lasers: manifolds, bifurcations and symbolic dynamics. Zbl 1106.34320Collins, Pieter; Krauskopf, Bernd 1 2005 A vector field model of a saddle-node Hopf bifurcation with global reinjection. Zbl 1106.34316Oldeman, Bart; Krauskopf, Bernd 1 2005 Bifurcation analysis of an inverted pendulum with delayed feedback control near a triple-zero eigenvalue singularity. Zbl 1054.34121Sieber, Jan; Krauskopf, Bernd 32 2004 Computing one-dimensional stable manifolds and stable sets of planar maps without the inverse. Zbl 1059.37067England, J. P.; Krauskopf, B.; Osinga, H. M. 31 2004 Complex balancing motions of an inverted pendulum subject to delayed feedback control. Zbl 1070.34105Sieber, J.; Krauskopf, B. 9 2004 The Lorenz manifold as a collection of geodesic level sets. Zbl 1083.37019Krauskopf, Bernd; Osinga, Hinke M. 7 2004 Crocheting the Lorenz manifold. Zbl 1073.37036Osinga, Hinke M.; Krauskopf, Bernd 5 2004 One-dimensional unstable eigenfunction and manifold computations in delay differential equations. Zbl 1052.65115Green, Kirk; Krauskopf, Bernd; Engelborghs, Koen 5 2004 A planar model system for the saddle-node Hopf bifurcation with global reinjection. Zbl 1061.37028Krauskopf, Bernd; Oldeman, Bart E. 4 2004 Computing geodesic level sets on global (un)stable manifolds of vector fields. Zbl 1089.37014Krauskopf, Bernd; Osinga, Hinke M. 22 2003 Computing unstable manifolds of periodic orbits in delay differential equations. Zbl 1017.65102Krauskopf, Bernd; Green, Kirk 14 2003 Homoclinic branch switching: a numerical implementation of Lin’s method. Zbl 1057.37073Oldeman, Bart E.; Champneys, Alan R.; Krauskopf, Bernd 11 2003 A two-parameter study of the locking region of a semiconductor laser subject to phase-conjugate feedback. Zbl 1088.37522Green, Kirk; Krauskopf, Bernd; Samaey, Giovanni 6 2003 Nonlinear dynamics and chaos: Where do we go from here? Zbl 0996.00035 2 2003 Bifurcation analysis of frequency locking in a semiconductor laser with phase-conjugate feedback. Zbl 1046.37508Green, Kirk; Krauskopf, Bernd 2 2003 Bistability and torus break-up in a semiconductor laser with phase-conjugate feedback. Zbl 1023.34064Green, Kirk; Krauskopf, Bernd; Engelborghs, Koen 7 2002 Accumulating regions of winding periodic orbits in optically driven lasers. Zbl 1047.78502Krauskopf, Bernd; Wieczorek, Sebastian 5 2002 Global quantitative predictions of complex laser dynamics. Zbl 1244.78008Wieczorek, Sebastian; Simpson, Thomas B.; Krauskopf, Bernd; Lenstra, Daan 5 2002 Numerical unfoldings of codimension-three resonant homoclinic flip bifurcations. Zbl 0990.37039Oldeman, Bart E.; Krauskopf, Bernd; Champneys, Alan R. 33 2001 Global analysis of dynamical systems. Festschrift dedicated to Floris Takens for his 60th birthday. Zbl 0971.00062 3 2001 Strong resonances and Takens’s Utrecht preprint. Zbl 1193.37067Krauskopf, Bernd 2 2001 Resonant homoclinic flip bifurcations. Zbl 0990.37038Homburg, Ale Jan; Krauskopf, Bernd 48 2000 Death of period-doublings: Locating the homoclinic-doubling cascade. Zbl 1011.34036Oldeman, Bart E.; Krauskopf, Bernd; Champneys, Alan R. 12 2000 Investigating torus bifurcations in the forced Van der Pol oscillator. Zbl 0987.37079Krauskopf, Bernd; Osinga, Hinke M. 9 2000 Two-dimensional global manifolds of vector fields. Zbl 0983.37110Krauskopf, Bernd; Osinga, Hinke 33 1999 Hausdorff convergence of Julia sets. Zbl 0915.58085Krauskopf, Bernd; Kriete, Hartje 7 1999 Growing 1D and quasi-2D unstable manifolds of maps. Zbl 0915.65075Krauskopf, Bernd; Osinga, Hinke 41 1998 Global study of a family of cubic Liénard equations. Zbl 0920.58034Khibnik, Alexander I.; Krauskopf, Bernd; Rousseau, Christiane 26 1998 ...and 10 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,150 Authors 56 Krauskopf, Bernd 40 Osinga, Hinke Maria 18 Algaba, Antonio 17 Kühn, Christian 17 Rodríguez-Luis, Alejandro J. 16 Wechselberger, Martin 16 Zhu, Deming 14 Desroches, Mathieu 14 Mireles-James, Jason D. 12 Sieber, Jan 11 Vo, Theodore 10 Krupa, Martin 10 Merino, Manuel 8 Liu, Xingbo 8 Qin, Bo-Wei 8 Zhang, Tiansi 7 Humphries, Antony R. 7 Kirk, Vivien 7 Llibre, Jaume 7 Rubin, Jonathan E. 6 Aguirre, Pablo 6 Boussaada, Islam 6 Chen, Hebai 6 Chung, Kwok-Wai 6 Freire Macías, Emilio 6 Hüls, Thorsten 6 Inaba, Naohiko 6 Kuznetsov, Yuri Alexandrovich 6 Kyrychko, Yuliya N. 6 Lloyd, David J. B. 6 Niculescu, Silviu-Iulian 6 Páez Chávez, Joseph Nikolai 6 Schöll, Eckehard 6 Stépán, Gábor 6 Yanchuk, Sergiĭ Volodymyrovych 5 Ashwin, Peter 5 Barrio, Roberto 5 Barton, David A. W. 5 Bi, Qinsheng 5 Champneys, Alan R. 5 Gamero, Estanislao 5 Green, Kirk 5 Hittmeyer, Stefanie 5 Jardón-Kojakhmetov, Hildeberto 5 Kaper, Tasso J. 5 Keane, Andrew 5 Knobloch, Jürgen 5 Lessard, Jean-Philippe 5 Ponce, Enrique 5 Postlethwaite, Claire M. 5 Rodrigues, Serafim 5 Tsaneva-Atanasova, Krasimira T. 4 Avitabile, Daniele 4 Barabash, Nikita V. 4 Belykh, Vladimir Nikitich 4 Bertram, Richard 4 Blyuss, Konstantin B. 4 de la Llave, Rafael 4 Dellnitz, Michael 4 Doedel, Eusebius J. 4 Ersöz, Elif Köksal 4 Fernández-García, Soledad 4 Giraldo, Andrus 4 Guckenheimer, John M. 4 Homburg, Ale Jan 4 Insperger, Tamás 4 Knobloch, Edgar 4 Kousaka, Takuji 4 Krupa, Maciej 4 Li, Chengzhi 4 Liu, Yang 4 Macau, Elbert E. N. 4 Mann, Brian P. 4 Meijer, Hil G. E. 4 Mezić, Igor 4 Naudot, Vincent 4 Neild, Simon A. 4 Oldeman, Bart E. 4 Sadhu, Susmita 4 Tabak, Joël 4 Teruel, Antonio E. 4 Touboul, Jonathan David 3 Balasuriya, Sanjeeva 3 Banerjee, Soumitro 3 Belhaq, Mohamed 3 Belykh, Igor V. 3 Berglund, Nils 3 Broderick, Neil G. R. 3 Broer, Henk W. 3 Campbell, Sue Ann 3 Cao, Jinde 3 Carmona, Victoriano 3 Chekroun, Mickaël D. 3 Chen, Fangqi 3 Chen, Xingwu 3 Coombes, Stephen 3 Dijkstra, Henk A. 3 Domínguez-Moreno, María C. 3 Dumortier, Freddy 3 Engel, Maximilian ...and 1,050 more Authors all top 5 Cited in 131 Serials 89 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 65 Physica D 58 Chaos 55 SIAM Journal on Applied Dynamical Systems 31 Nonlinear Dynamics 28 Communications in Nonlinear Science and Numerical Simulation 19 Journal of Differential Equations 17 Journal of Nonlinear Science 16 Chaos, Solitons and Fractals 16 Journal of Dynamics and Differential Equations 14 Dynamical Systems 14 Discrete and Continuous Dynamical Systems. Series B 11 Nonlinearity 10 Journal of Computational Dynamics 10 Philosophical Transactions of the Royal Society of London. A. 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Zeitschrift für angewandte Mathematik und Physik 1 Mathematics of Computation 1 BIT 1 Duke Mathematical Journal 1 International Journal for Numerical Methods in Engineering 1 Mathematische Zeitschrift 1 Meccanica 1 Numerical Functional Analysis and Optimization 1 Ricerche di Matematica 1 Tokyo Journal of Mathematics 1 Transactions of the American Mathematical Society 1 Applied Mathematics and Mechanics. (English Edition) 1 Computational Mechanics 1 Journal of Economic Dynamics & Control 1 Mathematical and Computer Modelling 1 Dynamics and Stability of Systems 1 SIAM Journal on Matrix Analysis and Applications 1 Sugaku Expositions 1 Numerical Algorithms 1 Automation and Remote Control 1 Linear Algebra and its Applications 1 Bulletin of the American Mathematical Society. New Series 1 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 1 Celestial Mechanics and Dynamical Astronomy 1 International Journal of Robust and Nonlinear Control ...and 31 more Serials all top 5 Cited in 38 Fields 388 Dynamical systems and ergodic theory (37-XX) 387 Ordinary differential equations (34-XX) 138 Biology and other natural sciences (92-XX) 91 Numerical analysis (65-XX) 66 Mechanics of particles and systems (70-XX) 57 Systems theory; control (93-XX) 45 Partial differential equations (35-XX) 26 Fluid mechanics (76-XX) 20 Statistical mechanics, structure of matter (82-XX) 19 Mechanics of deformable solids (74-XX) 18 Optics, electromagnetic theory (78-XX) 13 Operations research, mathematical programming (90-XX) 11 Geophysics (86-XX) 10 Functions of a complex variable (30-XX) 10 Probability theory and stochastic processes (60-XX) 10 Information and communication theory, circuits (94-XX) 8 Difference and functional equations (39-XX) 8 Calculus of variations and optimal control; optimization (49-XX) 6 Computer science (68-XX) 5 General and overarching topics; collections (00-XX) 5 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 4 Integral equations (45-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Approximations and expansions (41-XX) 3 Operator theory (47-XX) 3 Differential geometry (53-XX) 3 Global analysis, analysis on manifolds (58-XX) 3 Astronomy and astrophysics (85-XX) 2 Algebraic topology (55-XX) 2 Manifolds and cell complexes (57-XX) 2 Quantum theory (81-XX) 1 History and biography (01-XX) 1 Real functions (26-XX) 1 Measure and integration (28-XX) 1 Geometry (51-XX) 1 General topology (54-XX) 1 Statistics (62-XX) 1 Classical thermodynamics, heat transfer (80-XX) Citations by Year