Edit Profile Champneys, Alan R. Compute Distance To: Compute Author ID: champneys.alan-r Published as: Champneys, A.; Champneys, A. R.; Champneys, Alan; Champneys, Alan R. Documents Indexed: 121 Publications since 1991, including 4 Books all top 5 Co-Authors 8 single-authored 12 Thompson, John Michael T. 11 Hunt, Giles W. 9 Lord, Gabriel James 8 di Bernardo, Mario 6 Budd, Christopher John 6 Oldeman, Bart E. 6 van der Heijden, Gert H. M. 5 Fraser, Wynstone Barrie 5 Homer, Martin E. 5 Krauskopf, Bernd 5 Malomed, Boris A. 5 Nordmark, Arne B. 5 Sandstede, Björn 4 Avitabile, Daniele 4 Kuznetsov, Yuri Alexandrovich 4 Melvin, Thomas R. O. 4 Piiroinen, Petri T. 3 Friswell, Michael Ian 3 Hös, Csaba J. 3 Kirk, Vivien 3 Knobloch, Edgar 3 Kowalczyk, Piotr 3 Lloyd, David J. B. 3 McKenna, Patrick Joseph 3 Toland, John Francis 3 Wagenknecht, Thomas 3 Yang, Jianke 2 Acheson, David J. 2 Bazsó, Csaba 2 Breña-Medina, Víctor F. 2 Buryak, Alexander V. 2 Dankowicz, Harry J. 2 Eyres, R. D. 2 Härterich, Jörg M. 2 Kaup, David J. 2 Lieven, Nick A. J. 2 Pelinovsky, Dmitry Efimovich 2 Rothos, Vassilis M. 2 Spence, Alastair 2 Szalai, Róbert 2 Várkonyi, Péter László 2 Verschueren, Nicolas 2 Wagg, David J. 2 Ward, Michael J. 2 Wilson, Richard Eddie 2 Woods, P. D. 1 Aigner, Andreas A. 1 Bai, Fengshan 1 Beyn, Wolf-Jürgen 1 Briant, Linford J. B. 1 Buffoni, Boris 1 Cammarano, Andrea 1 Cooper, N. P. 1 Crowdy, Darren Gregory 1 Cuevas Maraver, Jesús 1 Dawes, Jonathan H. P. 1 Demirel, Güven 1 Desroches, Mathieu 1 Doedel, Eusebius J. 1 Domínguez, Jaime 1 Escalona, José Luis 1 Gaitonde, Ann L. 1 Galán-Vioque, Jorge 1 Galán, Jorge E. 1 Galán, José 1 Govaerts, Willy J. F. 1 Green, K. L. 1 Green, Kevin R. 1 Grierson, C. 1 Gross, Thilo 1 Groves, Mark D. 1 Harris, Simon C. 1 Hill, Thomas L. 1 Hjorth, Poul G. 1 Hogan, John Wesley 1 Hogan, S. John 1 Jeffrey, Mike R. 1 Jones, David Pierce 1 Kennedy, H. J. 1 Kevrekidis, Panayotis G. 1 Kolossovski, K. Y. 1 Kullmann, László 1 Kyrychko, Yulia 1 Linaro, Daniele 1 Lowenberg, Mark H. 1 Lust, Kurt 1 Ma, Yongpei 1 MacCarthy, Bart L. 1 Man, Harry 1 Melcher, John 1 Miles, M. J. 1 Mullin, Tom 1 Muñoz, A. M. 1 Neild, Simon A. 1 Osinga, Hinke Maria 1 Papageorgiou, Demetrius 1 Paton, Julian F. R. 1 Payton, O. 1 Pearce, M. J. 1 Peletier, Mark Adriaan ...and 29 more Co-Authors all top 5 Serials 17 Physica D 13 SIAM Journal on Applied Dynamical Systems 8 Nonlinearity 8 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 7 IMA Journal of Applied Mathematics 6 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 4 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 3 SIAM Journal on Applied Mathematics 3 Journal of Nonlinear Science 3 Nonlinear Dynamics 2 International Journal of Solids and Structures 2 Journal of Fluid Mechanics 2 Dynamics and Stability of Systems 2 Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 2 SIAM Journal on Scientific Computing 2 Chaos 2 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 1 Computer Methods in Applied Mechanics and Engineering 1 International Journal of Mechanical Sciences 1 International Journal of Non-Linear Mechanics 1 International Journal for Numerical Methods in Fluids 1 Journal of the Mechanics and Physics of Solids 1 Journal of Sound and Vibration 1 Physics Letters. A 1 Chaos, Solitons and Fractals 1 Mathematics and Computers in Simulation 1 Ergodic Theory and Dynamical Systems 1 CWI Quarterly 1 Journal of Physics A: Mathematical and General 1 SIAM Review 1 Journal of Dynamics and Differential Equations 1 Philosophical Transactions of the Royal Society of London. Series A 1 Advances in Computational Mathematics 1 The ANZIAM Journal 1 Advanced Series in Nonlinear Dynamics 1 Applied Mathematical Sciences 1 Discrete and Continuous Dynamical Systems. Series S 1 Journal of Theoretical Biology 1 Boletín de la Sociedad Española de Matemática Aplicada. S\(\vec{\text{e}}\)MA 1 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences all top 5 Fields 50 Dynamical systems and ergodic theory (37-XX) 43 Ordinary differential equations (34-XX) 36 Mechanics of deformable solids (74-XX) 30 Partial differential equations (35-XX) 21 Mechanics of particles and systems (70-XX) 13 Numerical analysis (65-XX) 11 Fluid mechanics (76-XX) 8 Optics, electromagnetic theory (78-XX) 5 General and overarching topics; collections (00-XX) 4 Biology and other natural sciences (92-XX) 3 History and biography (01-XX) 2 Statistical mechanics, structure of matter (82-XX) 2 Information and communication theory, circuits (94-XX) 1 Combinatorics (05-XX) 1 Group theory and generalizations (20-XX) 1 Difference and functional equations (39-XX) 1 Probability theory and stochastic processes (60-XX) 1 Quantum theory (81-XX) 1 Geophysics (86-XX) 1 Operations research, mathematical programming (90-XX) 1 Systems theory; control (93-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH 103 Publications have been cited 2,010 times in 1,430 Documents Cited by ▼ Year ▼ Piecewise-smooth dynamical systems. Theory and applications. Zbl 1146.37003di Bernardo, M.; Budd, C. J.; Champneys, A. R.; Kowalczyk, P. 562 2008 Bifurcations in nonsmooth dynamical systems. Zbl 1168.34006di Bernardo, Mario; Budd, Chris J.; Champneys, Alan R.; Kowalczyk, Piotr; Nordmark, Arne B.; Tost, Gerard Olivar; Piiroinen, Petri T. 106 2008 Normal form maps for grazing bifurcations in \(n\)-dimensional piecewise-smooth dynamical systems. Zbl 1067.37063di Bernardo, M.; Budd, C. J.; Champneys, A. R. 69 2001 Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics. Zbl 1194.37154Champneys, A. R. 68 1998 A numerical toolbox for homoclinic bifurcation analysis. Zbl 0877.65058Champneys, A. R.; Kuznetsov, Yu. A.; Sandstede, B. 66 1996 Numerical detection and continuation of codimension-two homoclinic bifurcations. Zbl 0873.34030Champneys, A. R.; Kuznetsov, Yu. A. 61 1994 Bifurcation and coalescence of a plethora of homoclinic orbits for a Hamiltonian system. Zbl 0854.34047Buffoni, B.; Champneys, A. R.; Toland, J. F. 57 1996 Heteroclinic tangles and homoclinic snaking in the unfolding of a degenerate reversible Hamiltonian-Hopf bifurcation. Zbl 0952.37009Woods, P. D.; Champneys, A. R. 48 1999 Grazing, skipping and sliding: Analysis of the non-smooth dynamics of the DC/DC buck converter. Zbl 0904.34034di Bernardo, Mario; Budd, Chris; Champneys, Alan 47 1998 Cellular buckling in long structures. Zbl 0974.74024Hunt, G. W.; Peletier, M. A.; Champneys, A. R.; Woods, P. D.; Ahmer Wadee, M.; Budd, C. J.; Lord, G. J. 46 2000 Localized hexagon patterns of the planar Swift-Hohenberg equation. Zbl 1168.35311Lloyd, David J. B.; Sandstede, Björn; Avitabile, Daniele; Champneys, Alan R. 40 2008 A global investigation of solitary-wave solutions to a two-parameter model for water waves. Zbl 0913.76010Champneys, Alan R.; Groves, Mark D. 36 1997 Corner collision implies border-collision bifurcation. Zbl 0984.34028di Bernardo, M.; Budd, C. J.; Champneys, A. R. 34 2001 Bifurcation of a plethora of multi-modal homoclinic orbits for autonomous Hamiltonian systems. Zbl 0789.58035Champneys, A. R.; Toland, J. F. 34 1993 Numerical continuation, and computation of normal forms. Zbl 1034.37048Beyn, Wolf-Jürgen; Champneys, Alan; Doedel, Eusebius; Govaerts, Willy; Kuznetsov, Yuri A.; Sandstede, Björn 32 2002 Numerical unfoldings of codimension-three resonant homoclinic flip bifurcations. Zbl 0990.37039Oldeman, Bart E.; Krauskopf, Bernd; Champneys, Alan R. 30 2001 Embedded solitons: Solitary waves in resonance with the linear spectrum. Zbl 0976.35087Champneys, A. R.; Malomed, B. A.; Yang, J.; Kaup, D. J. 28 2001 Two-parameter discontinuity-induced bifurcations of limit cycles: classification and open problems. Zbl 1141.37341Kowalczyk, P.; Di Bernardo, M.; Champneys, A. R.; Hogan, S. J.; Homer, M.; Piiroinen, P. T.; Kuznetsov, Yu. A.; Nordmark, A. 26 2006 Codimension-two homoclinic bifurcations underlying spike adding in the Hindmarsh-Rose burster. Zbl 1263.37036Linaro, Daniele; Champneys, Alan; Desroches, Mathieu; Storace, Marco 21 2012 Computation of homoclinic solutions to periodic orbits in a reduced water-wave problem. Zbl 0888.34040Champneys, A. R.; Lord, G. J. 21 1997 From helix to localized writhing in the torsional post-buckling of elastic rods. Zbl 0946.74025Thompson, J. M. T.; Champneys, A. R. 21 1996 When Shil’nikov meets Hopf in excitable systems. Zbl 1170.34025Champneys, Alan R.; Kirk, Vivien; Knobloch, Edgar; Oldeman, Bart E.; Sneyd, James 17 2007 The entwined wiggling of homoclinic curves emerging from saddle-node/Hopf instabilities. Zbl 1051.37023Champneys, A. R.; Kirk, V. 17 2004 Homoclinic and heteroclinic orbits underlying the post-buckling of axially-compressed cylindrical shells. Zbl 0958.74021Hunt, G. W.; Lord, G. J.; Champneys, A. R. 17 1999 Algebra, analysis and probability for a coupled system of reaction- diffusion equations. Zbl 0824.60070Champneys, Alan; Harris, Simon; Toland, John; Warren, Jonathan; Williams, David 17 1995 Chaos and period-adding; experimental and numerical verification of the grazing bifurcation. Zbl 1125.70015Piiroinen, P. T.; Virgin, L. N.; Champneys, A. R. 16 2004 Do true elevation gravity-capillary solitary waves exist? A numerical investigation. Zbl 1023.76011Champneys, A. R.; Vanden-Broeck, J.-M.; Lord, G. J. 15 2002 Multiple solitary waves due to second-harmonic generation in quadratic media. Zbl 0923.35169Yew, A. C.; Champneys, A. R.; McKenna, P. J. 14 1999 Numerical computation of coherent structures. Zbl 1129.65071Champneys, Alan R.; Sandstede, Björn 13 2007 Spatially complex localisation in twisted elastic rods constrained to a cylinder. Zbl 1006.74521van der Heijden, G. H. M.; Champneys, A. R.; Thompson, J. M. T. 13 2002 Multi-pulse embedded solitons as bound states of quasi-solitons. Zbl 1010.35087Kolossovski, K.; Champneys, A. R.; Buryak, A. V.; Sammut, R. A. 13 2002 Codimension-one persistence beyond all orders of homoclinic orbits to singular saddle centres in reversible systems. Zbl 0985.37045Champneys, A. R. 13 2001 Solitary waves in nonlinear beam equations: Stability, fission and fusion. Zbl 0974.74034Champneys, A. R.; McKenna, P. J.; Zegeling, P. A. 13 2000 The non-transverse Shil’nikov-Hopf bifurcation: uncoupling of homoclinic orbits and homoclinic tangencies. Zbl 0986.37041Champneys, A. R.; Rodríguez-Luis, A. J. 13 1999 A new barrier to the existence of moving kinks in Frenkel-Kontorova lattices. Zbl 1037.74026Aigner, A. A.; Champneys, A. R.; Rothos, V. M. 12 2003 Death of period-doublings: Locating the homoclinic-doubling cascade. Zbl 1011.34036Oldeman, Bart E.; Krauskopf, Bernd; Champneys, Alan R. 12 2000 Computation of localized post buckling in long axially compressed cylindrical shells. Zbl 0894.73040Lord, G. J.; Champneys, A. R.; Hunt, G. W. 12 1997 Hunting for homoclinic orbits in reversible systems: A shooting technique. Zbl 0824.65080Champneys, Alan R.; Spence, Alastair 12 1993 Discontinuity-induced bifurcations in systems with impacts and friction: discontinuities in the impact law. Zbl 1203.70027Nordmark, Arne; Dankowicz, Harry; Champneys, Alan 11 2009 Travelling solitary waves in the discrete Schrödinger equation with saturable nonlinearity: Existence, stability and dynamics. Zbl 1167.35448Melvin, T. R. O.; Champneys, A. R.; Kevrekidis, P. G.; Cuevas, J. 11 2008 Embedded solitons: A new type of solitary wave. Zbl 0976.35059Yang, J.; Malomed, B. A.; Kaup, D. J.; Champneys, A. R. 11 2001 Localization and solitary waves in solid mechanics. Zbl 0949.00014Champneys, A. R. (ed.); Hunt, G. W. (ed.); Thompson, J. M. T. (ed.) 11 1999 Moving embedded solitons. Zbl 0969.35113Champneys, Alan R.; Malomed, Boris A. 11 1999 Spatially complex localization after one-twist-per-wave equilibria in twisted circular rods with initial curvature. Zbl 0902.73044Champneys, A. R.; van der Heijden, G. H. M.; Thompson, J. M. T. 11 1997 The Painlevé paradox in contact mechanics. Zbl 1408.70006Champneys, Alan R.; Várkonyi, Péter L. 10 2016 Friction-induced reverse chatter in rigid-body mechanisms with impacts. Zbl 1385.70030Nordmark, Arne; Dankowicz, Harry; Champneys, Alan 10 2011 Cascades of homoclinic orbits to a saddle-centre for reversible and perturbed Hamiltonian systems. Zbl 1003.37033Champneys, Alan R.; Härterich, Jörg 10 2000 A non-transverse homoclinic orbit to a saddle-node equilibrium. Zbl 0853.58079Champneys, Alan R.; Härterich, Jörg; Sandstede, Björn 10 1996 The use of normal forms for analysing nonlinear mechanical vibrations. Zbl 1353.70052Neild, Simon A.; Champneys, Alan R.; Wagg, David J.; Hill, Thomas L.; Cammarano, Andrea 9 2015 Numerical continuation of high Reynolds number external flows. Zbl 1426.76435Wales, C.; Gaitonde, A. L.; Jones, D. P.; Avitabile, D.; Champneys, A. R. 9 2012 Unfolding a tangent equilibrium-to-periodic heteroclinic cycle. Zbl 1187.34056Champneys, Alan R.; Kirk, Vivien; Knobloch, Edgar; Oldeman, Bart E.; Rademacher, J. D. M. 9 2009 Homoclinic branch switching: a numerical implementation of Lin’s method. Zbl 1057.37073Oldeman, Bart E.; Champneys, Alan R.; Krauskopf, Bernd 9 2003 When gap solitons become embedded solitons: A generic unfolding. Zbl 1011.37037Wagenknecht, T.; Champneys, A. R. 9 2003 A multipicity of localized buckling modes for twisted rod equations. Zbl 0872.73015Champneys, A. R.; Thompson, J. M. T. 9 1996 Subsidiary homoclinic orbits to a saddle-focus for reversible systems. Zbl 0873.34037Champneys, A. R. 9 1994 A Newton-Picard shooting method for computing periodic solutions of large-scale dynamical systems. Zbl 1080.65542Roose, D.; Lust, K.; Champneys, A.; Spence, A. 8 1995 Stripe to spot transition in a plant root hair initiation model. Zbl 06444870Breña-Medina, V. F.; Avitabile, D.; Champneys, A. R.; Ward, M. J. 6 2015 Mathematical modeling of plant root hair initiation: dynamics of localized patches. Zbl 1302.35030Breña-Medina, V.; Champneys, A. R.; Grierson, C.; Ward, M. J. 6 2014 Discrete snaking: multiple cavity solitons in saturable media. Zbl 1193.35172Yulin, A. V.; Champneys, A. R. 6 2010 A model for cell polarization without mass conservation. Zbl 1386.35013Verschueren, Nicolas; Champneys, Alan 5 2017 Stability and bifurcation analysis of a spinning space tether. Zbl 1149.70316Valverde, J.; Escalona, J. L.; Dominguez, J.; Champneys, A. R. 5 2006 Boundary effects and the onset of Taylor vortices. Zbl 1098.76532Rucklidge, A. M.; Champneys, A. R. 5 2004 The ‘Indian wire trick’ via parametric excitation: a comparison between theory and experiment. Zbl 1047.70044Mullin, Tom; Champneys, Alan; Fraser, W. Barrie; Galan, Jorge; Acheson, David 5 2003 The spatial complexity of localized buckling in rods with noncircular cross-section. Zbl 0928.74033van der Heijden, G. H. M.; Champneys, A. R.; Thompson, J. M. T. 5 1999 On solitary waves of a piecewise linear suspended beam model. Zbl 0903.73031Champneys, A. R.; McKenna, P. J. 5 1997 Localization and solitary waves in solid mechanics. Zbl 0888.35094Champneys, A. R.; Hunt, G. W.; Thompson, J. M. T. 5 1997 Discrete traveling solitons in the Salerno model. Zbl 1171.34041Melvin, Thomas R. O.; Champneys, Alan R.; Pelinovsky, Dmitry E. 4 2009 Analysis of the transient response of an automatic dynamic balancer for eccentric rotors. Zbl 1192.70033Green, K.; Champneys, A. R.; Friswell, M. I. 4 2006 The parametrically excited upside-down rod: an elastic jointed pendulum model. Zbl 1236.74147Galán, J.; Fraser, W. B.; Acheson, D. J.; Champneys, A. R. 4 2005 Bifurcation analysis of surge and rotating stall in the Moore-Greitzer compression system. Zbl 1072.76065Hős, Csaba; Champneys, Alan; Kullmann, László 4 2003 A scalar nonlocal bifurcation of solitary waves for coupled nonlinear Schrödinger systems. Zbl 1021.35101Champneys, Alan R.; Yang, Jianke 4 2002 Homoclinic orbits in reversible systems. II: Multi-bumps and saddle-centres. Zbl 0998.37011Champneys, A. R. 4 1999 Computation of homoclinic orbits in partial differential equations: An application to cylindrical shell buckling. Zbl 0954.74021Lord, G. J.; Champneys, A. R.; Hunt, G. W. 4 1999 On the stability of solitary wave solutions of the fifth-order KdV equation. Zbl 1044.35516Buryak, A. V.; Champneys, A. R. 4 1997 Feedback-induced instability in tapping mode atomic force microscopy: theory and experiment. Zbl 1228.74058Payton, O.; Champneys, A. R.; Homer, M. E.; Picco, L.; Miles, M. J. 3 2011 One-parameter localized traveling waves in nonlinear Schrödinger lattices. Zbl 1142.34041Pelinovsky, Dmitry E.; Melvin, Thomas R. O.; Champneys, Alan R. 3 2007 Accumulation of embedded solitons in systems with quadratic nonlinearity. Zbl 1144.37382Malomed, B. A.; Wagenknecht, T.; Champneys, A. R.; Pearce, M. J. 3 2005 Modelling and dynamic response of a damper with relief valve. Zbl 1122.70018Eyres, R. D.; Champneys, A. R.; Lieven, N. A. J. 3 2005 Efficient numerical continuation and stability analysis of spatiotemporal quadratic optical solitons. Zbl 1096.78006Lloyd, D. J. B.; Champneys, A. R. 3 2005 Discrete embedded solitons. Zbl 1125.37051Yagasaki, Kazuyuki; Champneys, Alan R.; Malomed, Boris A. 3 2005 Robust heteroclinic cycles in the one-dimensional complex Ginzburg-Landau equation. Zbl 1070.35088Lloyd, D. J. B.; Champneys, A. R.; Wilson, R. E. 3 2005 The ‘Indian rope trick’ for a parametrically excited flexible rod: Linearized analysis. Zbl 0974.74029Champneys, Alan R.; Fraser, W. Barrie 3 2000 Asynchronous partial contact motion due to internal resonance in multiple degree-of-freedom rotordynamics. Zbl 1371.70058Shaw, A. D.; Champneys, A. R.; Friswell, M. I. 2 2016 The impacting cantilever: modal non-convergence and the importance of stiffness matching. Zbl 1325.74113Melcher, John; Champneys, Alan R.; Wagg, David J. 2 2013 Nonlinear models of development, amplification and compression in the mammalian cochlea. Zbl 1239.92025Szalai, R.; Tsaneva-Atanasova, K.; Homer, M. E.; Champneys, A. R.; Kennedy, H. J.; Cooper, N. P. 2 2011 Snake-to-isola transition and moving solitons via symmetry-breaking in discrete optical cavities. Zbl 1223.37033Yulin, Alexey; Champneys, Alan 2 2011 Grazing bifurcations and chaos in the dynamics of a hydraulic damper with relief valves. Zbl 1090.37058Eyres, R. D.; Piiroinen, P. T.; Champneys, A. R.; Lieven, N. A. J. 2 2005 Nonlinear dynamics and chaos: Where do we go from here? Zbl 0996.00035Hogan, John (ed.); Champneys, Alan (ed.); Krauskopf, Bernd (ed.); di Bernardo, Mario (ed.); Wilson, Eddie (ed.); Osinga, Hinke (ed.); Homer, Martin (ed.) 2 2003 The ‘Indian rope trick’ for a parametrically excited flexible rod: nonlinear and subharmonic analysis. Zbl 1056.74041Fraser, W. Barrie; Champneys, Alan R. 2 2002 Introduction [to: Localization and solitary waves in solid mechanics]. Zbl 1166.35366Champneys, A. R. (ed.); Hunt, G. W. (ed.); Thompson, J. M. T. (ed.) 2 1999 Spatially complex localisation in twisted elastic rods constrained to lie in the plane. Zbl 0962.74033van der Heijden, G. H. M.; Champneys, A. R.; Thompson, J. M. T. 2 1999 Numerical detection and continuation of saddle-node homoclinic bifurcations of codimension one and two. Zbl 0867.34036Bai, Fengshan; Champneys, Alan R. 2 1996 Homoclinic orbits in the dynamics of articulated pipes conveying fluid. Zbl 0735.76005Champneys, Alan R. 2 1991 Revealing instabilities in a generalized triadic supply network: a bifurcation analysis. Zbl 1396.90006Ritterskamp, Daniel; Demirel, Güven; MacCarthy, Bart L.; Rudolf, Lars; Champneys, Alan R.; Gross, Thilo 1 2018 Dynamics beyond dynamic jam; unfolding the Painlevé paradox singularity. Zbl 1393.70032Nordmark, Arne; Várkonyi, Peter L.; Champneys, Alan R. 1 2018 A phase-plane analysis of localized frictional waves. Zbl 1404.74070Putelat, T.; Dawes, J. H. P.; Champneys, A. R. 1 2017 Bifurcation analysis of a simplified model of a pressure relief valve attached to a pipe. Zbl 1348.37082Bazsó, Csaba; Champneys, Alan R.; Hös, Csaba J. 1 2014 Investigation of a multi-ball, automatic dynamic balancing mechanism for eccentric rotors. Zbl 1153.74325Green, K.; Champneys, A. R.; Friswell, M. I.; Muñoz, A. M. 1 2008 Resonance tongue interaction in the parametrically excited column. Zbl 1126.74018Champneys, A. R.; Fraser, W. B. 1 2004 The torsional buckling and writhing of a simply supported rod hanging under gravity. Zbl 1004.74034Stump, D. M.; Champneys, A. R.; van der Heijden, G. H. M. 1 2001 Revealing instabilities in a generalized triadic supply network: a bifurcation analysis. Zbl 1396.90006Ritterskamp, Daniel; Demirel, Güven; MacCarthy, Bart L.; Rudolf, Lars; Champneys, Alan R.; Gross, Thilo 1 2018 Dynamics beyond dynamic jam; unfolding the Painlevé paradox singularity. Zbl 1393.70032Nordmark, Arne; Várkonyi, Peter L.; Champneys, Alan R. 1 2018 A model for cell polarization without mass conservation. Zbl 1386.35013Verschueren, Nicolas; Champneys, Alan 5 2017 A phase-plane analysis of localized frictional waves. Zbl 1404.74070Putelat, T.; Dawes, J. H. P.; Champneys, A. R. 1 2017 The Painlevé paradox in contact mechanics. Zbl 1408.70006Champneys, Alan R.; Várkonyi, Péter L. 10 2016 Asynchronous partial contact motion due to internal resonance in multiple degree-of-freedom rotordynamics. Zbl 1371.70058Shaw, A. D.; Champneys, A. R.; Friswell, M. I. 2 2016 The use of normal forms for analysing nonlinear mechanical vibrations. Zbl 1353.70052Neild, Simon A.; Champneys, Alan R.; Wagg, David J.; Hill, Thomas L.; Cammarano, Andrea 9 2015 Stripe to spot transition in a plant root hair initiation model. Zbl 06444870Breña-Medina, V. F.; Avitabile, D.; Champneys, A. R.; Ward, M. J. 6 2015 Mathematical modeling of plant root hair initiation: dynamics of localized patches. Zbl 1302.35030Breña-Medina, V.; Champneys, A. R.; Grierson, C.; Ward, M. J. 6 2014 Bifurcation analysis of a simplified model of a pressure relief valve attached to a pipe. Zbl 1348.37082Bazsó, Csaba; Champneys, Alan R.; Hös, Csaba J. 1 2014 The impacting cantilever: modal non-convergence and the importance of stiffness matching. Zbl 1325.74113Melcher, John; Champneys, Alan R.; Wagg, David J. 2 2013 Codimension-two homoclinic bifurcations underlying spike adding in the Hindmarsh-Rose burster. Zbl 1263.37036Linaro, Daniele; Champneys, Alan; Desroches, Mathieu; Storace, Marco 21 2012 Numerical continuation of high Reynolds number external flows. Zbl 1426.76435Wales, C.; Gaitonde, A. L.; Jones, D. P.; Avitabile, D.; Champneys, A. R. 9 2012 Friction-induced reverse chatter in rigid-body mechanisms with impacts. Zbl 1385.70030Nordmark, Arne; Dankowicz, Harry; Champneys, Alan 10 2011 Feedback-induced instability in tapping mode atomic force microscopy: theory and experiment. Zbl 1228.74058Payton, O.; Champneys, A. R.; Homer, M. E.; Picco, L.; Miles, M. J. 3 2011 Nonlinear models of development, amplification and compression in the mammalian cochlea. Zbl 1239.92025Szalai, R.; Tsaneva-Atanasova, K.; Homer, M. E.; Champneys, A. R.; Kennedy, H. J.; Cooper, N. P. 2 2011 Snake-to-isola transition and moving solitons via symmetry-breaking in discrete optical cavities. Zbl 1223.37033Yulin, Alexey; Champneys, Alan 2 2011 Discrete snaking: multiple cavity solitons in saturable media. Zbl 1193.35172Yulin, A. V.; Champneys, A. R. 6 2010 Discontinuity-induced bifurcations in systems with impacts and friction: discontinuities in the impact law. Zbl 1203.70027Nordmark, Arne; Dankowicz, Harry; Champneys, Alan 11 2009 Unfolding a tangent equilibrium-to-periodic heteroclinic cycle. Zbl 1187.34056Champneys, Alan R.; Kirk, Vivien; Knobloch, Edgar; Oldeman, Bart E.; Rademacher, J. D. M. 9 2009 Discrete traveling solitons in the Salerno model. Zbl 1171.34041Melvin, Thomas R. O.; Champneys, Alan R.; Pelinovsky, Dmitry E. 4 2009 Piecewise-smooth dynamical systems. Theory and applications. Zbl 1146.37003di Bernardo, M.; Budd, C. J.; Champneys, A. R.; Kowalczyk, P. 562 2008 Bifurcations in nonsmooth dynamical systems. Zbl 1168.34006di Bernardo, Mario; Budd, Chris J.; Champneys, Alan R.; Kowalczyk, Piotr; Nordmark, Arne B.; Tost, Gerard Olivar; Piiroinen, Petri T. 106 2008 Localized hexagon patterns of the planar Swift-Hohenberg equation. Zbl 1168.35311Lloyd, David J. B.; Sandstede, Björn; Avitabile, Daniele; Champneys, Alan R. 40 2008 Travelling solitary waves in the discrete Schrödinger equation with saturable nonlinearity: Existence, stability and dynamics. Zbl 1167.35448Melvin, T. R. O.; Champneys, A. R.; Kevrekidis, P. G.; Cuevas, J. 11 2008 Investigation of a multi-ball, automatic dynamic balancing mechanism for eccentric rotors. Zbl 1153.74325Green, K.; Champneys, A. R.; Friswell, M. I.; Muñoz, A. M. 1 2008 When Shil’nikov meets Hopf in excitable systems. Zbl 1170.34025Champneys, Alan R.; Kirk, Vivien; Knobloch, Edgar; Oldeman, Bart E.; Sneyd, James 17 2007 Numerical computation of coherent structures. Zbl 1129.65071Champneys, Alan R.; Sandstede, Björn 13 2007 One-parameter localized traveling waves in nonlinear Schrödinger lattices. Zbl 1142.34041Pelinovsky, Dmitry E.; Melvin, Thomas R. O.; Champneys, Alan R. 3 2007 Two-parameter discontinuity-induced bifurcations of limit cycles: classification and open problems. Zbl 1141.37341Kowalczyk, P.; Di Bernardo, M.; Champneys, A. R.; Hogan, S. J.; Homer, M.; Piiroinen, P. T.; Kuznetsov, Yu. A.; Nordmark, A. 26 2006 Stability and bifurcation analysis of a spinning space tether. Zbl 1149.70316Valverde, J.; Escalona, J. L.; Dominguez, J.; Champneys, A. R. 5 2006 Analysis of the transient response of an automatic dynamic balancer for eccentric rotors. Zbl 1192.70033Green, K.; Champneys, A. R.; Friswell, M. I. 4 2006 The parametrically excited upside-down rod: an elastic jointed pendulum model. Zbl 1236.74147Galán, J.; Fraser, W. B.; Acheson, D. J.; Champneys, A. R. 4 2005 Accumulation of embedded solitons in systems with quadratic nonlinearity. Zbl 1144.37382Malomed, B. A.; Wagenknecht, T.; Champneys, A. R.; Pearce, M. J. 3 2005 Modelling and dynamic response of a damper with relief valve. Zbl 1122.70018Eyres, R. D.; Champneys, A. R.; Lieven, N. A. J. 3 2005 Efficient numerical continuation and stability analysis of spatiotemporal quadratic optical solitons. Zbl 1096.78006Lloyd, D. J. B.; Champneys, A. R. 3 2005 Discrete embedded solitons. Zbl 1125.37051Yagasaki, Kazuyuki; Champneys, Alan R.; Malomed, Boris A. 3 2005 Robust heteroclinic cycles in the one-dimensional complex Ginzburg-Landau equation. Zbl 1070.35088Lloyd, D. J. B.; Champneys, A. R.; Wilson, R. E. 3 2005 Grazing bifurcations and chaos in the dynamics of a hydraulic damper with relief valves. Zbl 1090.37058Eyres, R. D.; Piiroinen, P. T.; Champneys, A. R.; Lieven, N. A. J. 2 2005 The entwined wiggling of homoclinic curves emerging from saddle-node/Hopf instabilities. Zbl 1051.37023Champneys, A. R.; Kirk, V. 17 2004 Chaos and period-adding; experimental and numerical verification of the grazing bifurcation. Zbl 1125.70015Piiroinen, P. T.; Virgin, L. N.; Champneys, A. R. 16 2004 Boundary effects and the onset of Taylor vortices. Zbl 1098.76532Rucklidge, A. M.; Champneys, A. R. 5 2004 Resonance tongue interaction in the parametrically excited column. Zbl 1126.74018Champneys, A. R.; Fraser, W. B. 1 2004 A new barrier to the existence of moving kinks in Frenkel-Kontorova lattices. Zbl 1037.74026Aigner, A. A.; Champneys, A. R.; Rothos, V. M. 12 2003 Homoclinic branch switching: a numerical implementation of Lin’s method. Zbl 1057.37073Oldeman, Bart E.; Champneys, Alan R.; Krauskopf, Bernd 9 2003 When gap solitons become embedded solitons: A generic unfolding. Zbl 1011.37037Wagenknecht, T.; Champneys, A. R. 9 2003 The ‘Indian wire trick’ via parametric excitation: a comparison between theory and experiment. Zbl 1047.70044Mullin, Tom; Champneys, Alan; Fraser, W. Barrie; Galan, Jorge; Acheson, David 5 2003 Bifurcation analysis of surge and rotating stall in the Moore-Greitzer compression system. Zbl 1072.76065Hős, Csaba; Champneys, Alan; Kullmann, László 4 2003 Nonlinear dynamics and chaos: Where do we go from here? Zbl 0996.00035Hogan, John (ed.); Champneys, Alan (ed.); Krauskopf, Bernd (ed.); di Bernardo, Mario (ed.); Wilson, Eddie (ed.); Osinga, Hinke (ed.); Homer, Martin (ed.) 2 2003 Numerical continuation, and computation of normal forms. Zbl 1034.37048Beyn, Wolf-Jürgen; Champneys, Alan; Doedel, Eusebius; Govaerts, Willy; Kuznetsov, Yuri A.; Sandstede, Björn 32 2002 Do true elevation gravity-capillary solitary waves exist? A numerical investigation. Zbl 1023.76011Champneys, A. R.; Vanden-Broeck, J.-M.; Lord, G. J. 15 2002 Spatially complex localisation in twisted elastic rods constrained to a cylinder. Zbl 1006.74521van der Heijden, G. H. M.; Champneys, A. R.; Thompson, J. M. T. 13 2002 Multi-pulse embedded solitons as bound states of quasi-solitons. Zbl 1010.35087Kolossovski, K.; Champneys, A. R.; Buryak, A. V.; Sammut, R. A. 13 2002 A scalar nonlocal bifurcation of solitary waves for coupled nonlinear Schrödinger systems. Zbl 1021.35101Champneys, Alan R.; Yang, Jianke 4 2002 The ‘Indian rope trick’ for a parametrically excited flexible rod: nonlinear and subharmonic analysis. Zbl 1056.74041Fraser, W. Barrie; Champneys, Alan R. 2 2002 Normal form maps for grazing bifurcations in \(n\)-dimensional piecewise-smooth dynamical systems. Zbl 1067.37063di Bernardo, M.; Budd, C. J.; Champneys, A. R. 69 2001 Corner collision implies border-collision bifurcation. Zbl 0984.34028di Bernardo, M.; Budd, C. J.; Champneys, A. R. 34 2001 Numerical unfoldings of codimension-three resonant homoclinic flip bifurcations. Zbl 0990.37039Oldeman, Bart E.; Krauskopf, Bernd; Champneys, Alan R. 30 2001 Embedded solitons: Solitary waves in resonance with the linear spectrum. Zbl 0976.35087Champneys, A. R.; Malomed, B. A.; Yang, J.; Kaup, D. J. 28 2001 Codimension-one persistence beyond all orders of homoclinic orbits to singular saddle centres in reversible systems. Zbl 0985.37045Champneys, A. R. 13 2001 Embedded solitons: A new type of solitary wave. Zbl 0976.35059Yang, J.; Malomed, B. A.; Kaup, D. J.; Champneys, A. R. 11 2001 The torsional buckling and writhing of a simply supported rod hanging under gravity. Zbl 1004.74034Stump, D. M.; Champneys, A. R.; van der Heijden, G. H. M. 1 2001 Cellular buckling in long structures. Zbl 0974.74024Hunt, G. W.; Peletier, M. A.; Champneys, A. R.; Woods, P. D.; Ahmer Wadee, M.; Budd, C. J.; Lord, G. J. 46 2000 Solitary waves in nonlinear beam equations: Stability, fission and fusion. Zbl 0974.74034Champneys, A. R.; McKenna, P. J.; Zegeling, P. A. 13 2000 Death of period-doublings: Locating the homoclinic-doubling cascade. Zbl 1011.34036Oldeman, Bart E.; Krauskopf, Bernd; Champneys, Alan R. 12 2000 Cascades of homoclinic orbits to a saddle-centre for reversible and perturbed Hamiltonian systems. Zbl 1003.37033Champneys, Alan R.; Härterich, Jörg 10 2000 The ‘Indian rope trick’ for a parametrically excited flexible rod: Linearized analysis. Zbl 0974.74029Champneys, Alan R.; Fraser, W. Barrie 3 2000 Heteroclinic tangles and homoclinic snaking in the unfolding of a degenerate reversible Hamiltonian-Hopf bifurcation. Zbl 0952.37009Woods, P. D.; Champneys, A. R. 48 1999 Homoclinic and heteroclinic orbits underlying the post-buckling of axially-compressed cylindrical shells. Zbl 0958.74021Hunt, G. W.; Lord, G. J.; Champneys, A. R. 17 1999 Multiple solitary waves due to second-harmonic generation in quadratic media. Zbl 0923.35169Yew, A. C.; Champneys, A. R.; McKenna, P. J. 14 1999 The non-transverse Shil’nikov-Hopf bifurcation: uncoupling of homoclinic orbits and homoclinic tangencies. Zbl 0986.37041Champneys, A. R.; Rodríguez-Luis, A. J. 13 1999 Localization and solitary waves in solid mechanics. Zbl 0949.00014Champneys, A. R. (ed.); Hunt, G. W. (ed.); Thompson, J. M. T. (ed.) 11 1999 Moving embedded solitons. Zbl 0969.35113Champneys, Alan R.; Malomed, Boris A. 11 1999 The spatial complexity of localized buckling in rods with noncircular cross-section. Zbl 0928.74033van der Heijden, G. H. M.; Champneys, A. R.; Thompson, J. M. T. 5 1999 Homoclinic orbits in reversible systems. II: Multi-bumps and saddle-centres. Zbl 0998.37011Champneys, A. R. 4 1999 Computation of homoclinic orbits in partial differential equations: An application to cylindrical shell buckling. Zbl 0954.74021Lord, G. J.; Champneys, A. R.; Hunt, G. W. 4 1999 Introduction [to: Localization and solitary waves in solid mechanics]. Zbl 1166.35366Champneys, A. R. (ed.); Hunt, G. W. (ed.); Thompson, J. M. T. (ed.) 2 1999 Spatially complex localisation in twisted elastic rods constrained to lie in the plane. Zbl 0962.74033van der Heijden, G. H. M.; Champneys, A. R.; Thompson, J. M. T. 2 1999 The role of homoclinic bifurcations in understanding the buckling of long thin cylindrical shells. Zbl 0982.74029Lord, G. J.; Champneys, A. R.; Hunt, G. W. 1 1999 Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics. Zbl 1194.37154Champneys, A. R. 68 1998 Grazing, skipping and sliding: Analysis of the non-smooth dynamics of the DC/DC buck converter. Zbl 0904.34034di Bernardo, Mario; Budd, Chris; Champneys, Alan 47 1998 A global investigation of solitary-wave solutions to a two-parameter model for water waves. Zbl 0913.76010Champneys, Alan R.; Groves, Mark D. 36 1997 Computation of homoclinic solutions to periodic orbits in a reduced water-wave problem. Zbl 0888.34040Champneys, A. R.; Lord, G. J. 21 1997 Computation of localized post buckling in long axially compressed cylindrical shells. Zbl 0894.73040Lord, G. J.; Champneys, A. R.; Hunt, G. W. 12 1997 Spatially complex localization after one-twist-per-wave equilibria in twisted circular rods with initial curvature. Zbl 0902.73044Champneys, A. R.; van der Heijden, G. H. M.; Thompson, J. M. T. 11 1997 On solitary waves of a piecewise linear suspended beam model. Zbl 0903.73031Champneys, A. R.; McKenna, P. J. 5 1997 Localization and solitary waves in solid mechanics. Zbl 0888.35094Champneys, A. R.; Hunt, G. W.; Thompson, J. M. T. 5 1997 On the stability of solitary wave solutions of the fifth-order KdV equation. Zbl 1044.35516Buryak, A. V.; Champneys, A. R. 4 1997 Localization and solitary waves in solid mechanics. Zbl 0886.00007Champneys, A. R. (ed.); Hunt, G. W. (ed.); Thompson, J. M. T. (ed.) 1 1997 A numerical toolbox for homoclinic bifurcation analysis. Zbl 0877.65058Champneys, A. R.; Kuznetsov, Yu. A.; Sandstede, B. 66 1996 Bifurcation and coalescence of a plethora of homoclinic orbits for a Hamiltonian system. Zbl 0854.34047Buffoni, B.; Champneys, A. R.; Toland, J. F. 57 1996 From helix to localized writhing in the torsional post-buckling of elastic rods. Zbl 0946.74025Thompson, J. M. T.; Champneys, A. R. 21 1996 A non-transverse homoclinic orbit to a saddle-node equilibrium. Zbl 0853.58079Champneys, Alan R.; Härterich, Jörg; Sandstede, Björn 10 1996 A multipicity of localized buckling modes for twisted rod equations. Zbl 0872.73015Champneys, A. R.; Thompson, J. M. T. 9 1996 Numerical detection and continuation of saddle-node homoclinic bifurcations of codimension one and two. Zbl 0867.34036Bai, Fengshan; Champneys, Alan R. 2 1996 Algebra, analysis and probability for a coupled system of reaction- diffusion equations. Zbl 0824.60070Champneys, Alan; Harris, Simon; Toland, John; Warren, Jonathan; Williams, David 17 1995 A Newton-Picard shooting method for computing periodic solutions of large-scale dynamical systems. Zbl 1080.65542Roose, D.; Lust, K.; Champneys, A.; Spence, A. 8 1995 Numerical detection and continuation of codimension-two homoclinic bifurcations. Zbl 0873.34030Champneys, A. R.; Kuznetsov, Yu. A. 61 1994 Subsidiary homoclinic orbits to a saddle-focus for reversible systems. Zbl 0873.34037Champneys, A. R. 9 1994 Bifurcation of a plethora of multi-modal homoclinic orbits for autonomous Hamiltonian systems. Zbl 0789.58035Champneys, A. R.; Toland, J. F. 34 1993 ...and 3 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,896 Authors 47 Llibre, Jaume 34 Champneys, Alan R. 27 Gardini, Laura 26 Simpson, David John Warwick 21 Teixeira, Marco Antonio 20 Jeffrey, Mike R. 19 Zhu, Deming 18 Sandstede, Björn 17 Avrutin, Viktor 17 Rodríguez-Luis, Alejandro J. 15 di Bernardo, Mario 15 Knobloch, Edgar 15 Páez Chávez, Joseph Nikolai 14 Han, Maoan 14 Ponce, Enrique 13 Chen, Hebai 13 Yang, Xiaosong 12 de Carvalho, Tiago 12 Sushko, Iryna 12 Tang, Sanyi 12 Zhusubaliev, Zhanybaĭ Tursunbaevich 11 Algaba, Antonio 11 Du, Zhengdong 11 Freire Macías, Emilio 11 Liu, Xingbo 11 Piiroinen, Petri T. 10 Hogan, S. John 10 Kooi, Bob W. 10 Krauskopf, Bernd 10 Kuznetsov, Yuri Alexandrovich 10 Novaes, Douglas Duarte 10 Osinga, Hinke Maria 10 Torregrosa, Joan 10 van der Heijden, Gert H. M. 10 Xiao, Yanni 10 Zhang, Xiang 9 Banerjee, Soumitro 9 Buzzi, Claudio Aguinaldo 9 Chen, Xingwu 9 Dankowicz, Harry J. 9 Dieci, Luca 9 Huan, Songmei 9 Kevrekidis, Panayotis G. 9 Kuske, Rachel A. 9 Liang, Feng 9 Schanz, Michael 9 Thompson, John Michael T. 9 Tonon, Durval José 9 Torres Peral, Francisco 9 Wagenknecht, Thomas 8 Boer, Martin P. 8 Huang, Lihong 8 Kowalczyk, Piotr 8 Malomed, Boris A. 8 Mosekilde, Erik 8 Pelinovsky, Dmitry Efimovich 8 van den Berg, Jan Bouwe 8 Wadee, M. Ahmer 8 Wen, Guilin 8 Xu, Yancong 8 Yagasaki, Kazuyuki 8 Yang, Jihua 8 Zhang, Tiansi 7 Aihara, Kazuyuki 7 Euzébio, Rodrigo D. 7 Fernández-Sánchez, Fernando 7 Glendinning, Paul Alexander 7 Knobloch, Jürgen 7 Li, Shimin 7 Luo, Albert C. J. 7 Merino, Manuel 7 Qin, Wenjie 7 Wiercigroch, Marian 7 Xie, Jianhua 7 Xiong, Yanqin 7 Yang, Jianke 6 Angulo, Fabiola 6 Avitabile, Daniele 6 Barrio, Roberto 6 Bassom, Andrew P. 6 Bergeon, Alain 6 Carter, Paul M. 6 Cheng, Sui Sun 6 Coombes, Stephen 6 Fečkan, Michal 6 Govaerts, Willy J. F. 6 Hosham, Hany A. 6 Kühn, Christian 6 Laing, Carlo R. 6 Lessard, Jean-Philippe 6 Nordmark, Arne B. 6 Tang, Guangyao 6 Tang, Yilei 6 Valls Anglés, Cláudia 6 Vanden-Broeck, Jean-Marc 6 Wadee, M. 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