Edit Profile (opens in new tab) Holmes, Philip J. Co-Author Distance Author ID: holmes.philip-j Published as: Holmes, Philip; Holmes, P.; Holmes, P. J.; Holmes, Philip J. more...less Homepage: https://www.princeton.edu/mae/people/faculty/holmes/ External Links: MGP · Wikidata · Math-Net.Ru · dblp · GND · IdRef Documents Indexed: 207 Publications since 1976, including 6 Books 3 Contributions as Editor · 2 Further Contributions Co-Authors: 124 Co-Authors with 163 Joint Publications 3,852 Co-Co-Authors all top 5 Co-Authors 35 single-authored 15 Lumley, John Leask 14 Berkooz, Gal 11 Domokos, Gábor 11 Marsden, Jerrold Eldon 7 Elezgaray, Juan 7 Schmitt, John M. 6 Ghigliazza, R. M. 6 Moehlis, Jeff 5 Guckenheimer, John M. 5 Smith, Troy R. 4 Cohen, Jonathan D. 4 Coller, B. D. 4 Doelman, Arjen 4 Duan, Jinqiao 4 Ghrist, Robert W. 4 Proctor, Joshua L. 4 Stone, Emily F. 4 Wong-Lin, Kongfatt 3 Aubry, Nadine 3 Bogacz, Rafal 3 Full, Robert J. 3 Goodman, Roy H. 3 Hek, Geertje 3 Hockett, Kevin G. 3 Kukillaya, Raghavendra P. 3 Mielke, Alexander 3 Rand, David A. 3 Simen, Patrick 3 Swart, Pieter J. 3 Weinstein, Michael I. 3 Wiggins, Stephen R. 3 Wittenberg, Ralf W. 2 Altendorfer, Richard 2 Aminzare, Zahra 2 Armbruster, Dieter 2 Campbell, Sue Ann 2 Cisternas, Jaime E. 2 Cohen, Avis H. 2 Dankowicz, Harry J. 2 Gao, Juan 2 Kutz, J. Nathan 2 Liu, Yuan Sophie 2 Moon, Francis C. 2 O’Reilly, Oliver Mary 2 Poje, Andrew C. 2 Rand, Richard H. 2 Royce, B. 2 Seipel, Justin E. 2 Srivastava, Vaibhav 2 Szeri, Andrew J. 2 Titi, Edriss Saleh 2 Veerman, Peter 1 Abraham, Ralph Herman 1 Alligood, Kathleen T. 1 Ball, John MacLeod 1 Ball, Rowena 1 Barnsley, Michael Fielding 1 Bélair, Jacques 1 Branner, Bodil 1 Broderick, Tamara 1 Brunsden, V. 1 Carroll, Thomas L. 1 Clarkson, B. L. 1 Coleman, Michael J. 1 Cortell, J. 1 Cusumano, Joseph P. 1 Devaney, Robert L. 1 Diacu, Florin Nicolae 1 Eckhoff, Philip 1 Faisst, Holger 1 Gilmore, Robert 1 Gilzenrat, Mark S. 1 Glass, Leon 1 Grebogi, Celso 1 Greenspan, B. D. 1 Greenspan, Bernie 1 Hanßmann, Heinz 1 Harris-Warrick, Ronald M. 1 Harrison, Jenny C. 1 Hoffman, Kathleen A. 1 Ilyashenko, Yulij Sergeevich 1 James, Richard D. 1 Jenkins, Jeffrey 1 Kalies, William D. 1 Keen, Linda 1 Kevrekidis, Ioannis George 1 Khibnik, Alexander I. 1 Kiemel, Tim 1 Kistner, A. 1 Koditschek, Dan 1 Lángi, Zsolt 1 Leibovich, Sidney 1 Leonard, Naomi Ehrich 1 Letellier, Christophe 1 Lozi, René 1 Mattingly, Jonathan Christopher 1 McMillen, Tyler 1 Medvedev, Georgi S. 1 Moser, Jürgen K. 1 Myers, Mark H. ...and 32 more Co-Authors all top 5 Serials 24 Physica D 8 Biological Cybernetics 8 Journal of Sound and Vibration 8 Journal of Nonlinear Science 7 International Journal of Non-Linear Mechanics 7 SIAM Journal on Applied Dynamical Systems 6 Neural Computation 5 Archive for Rational Mechanics and Analysis 5 Nonlinearity 5 SIAM Journal on Applied Mathematics 4 Journal of Applied Mechanics 4 Journal of Fluid Mechanics 4 Journal of Mathematical Psychology 4 SIAM Journal on Mathematical Analysis 4 Regular and Chaotic Dynamics 3 Journal of Mathematical Biology 3 Philosophical Transactions of the Royal Society of London. Ser. A 3 Quarterly of Applied Mathematics 3 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 3 Physics of Fluids 3 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 2 IMA Journal of Applied Mathematics 2 Theoretical and Computational Fluid Dynamics 2 Automatica 2 Journal of Differential Equations 2 SIAM Review 2 Nonlinear Dynamics 2 Journal of Theoretical Biology 1 Applied Scientific Research 1 Communications in Mathematical Physics 1 Computer Methods in Applied Mechanics and Engineering 1 Journal of Mathematical Physics 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Physics of Fluids 1 Quarterly Journal of Mechanics and Applied Mathematics 1 Rocky Mountain Journal of Mathematics 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Indiana University Mathematics Journal 1 Proceedings of the American Mathematical Society 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Studies in Applied Mathematics 1 Ergodic Theory and Dynamical Systems 1 IMA Journal of Mathematics Applied in Medicine and Biology 1 Mathematical and Computer Modelling 1 Dynamics and Stability of Systems 1 Neural Networks 1 European Journal of Applied Mathematics 1 Applied Mathematical Modelling 1 Journal of Dynamic Systems, Measurement and Control 1 Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 1 Journal of Dynamics and Differential Equations 1 Chaos 1 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Moscow Mathematical Journal 1 Stochastics and Dynamics 1 AMRX. Applied Mathematics Research eXpress 1 Applied Mathematical Sciences 1 Lecture Notes in Mathematics 1 Proceedings of Symposia in Applied Mathematics 1 Nonlinear Analysis. Theory, Methods & Applications 1 Cambridge Monographs on Mechanics all top 5 Fields 98 Dynamical systems and ergodic theory (37-XX) 62 Ordinary differential equations (34-XX) 42 Mechanics of particles and systems (70-XX) 38 Biology and other natural sciences (92-XX) 36 Fluid mechanics (76-XX) 30 Partial differential equations (35-XX) 27 Mechanics of deformable solids (74-XX) 11 Systems theory; control (93-XX) 8 Probability theory and stochastic processes (60-XX) 8 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 7 General and overarching topics; collections (00-XX) 5 Manifolds and cell complexes (57-XX) 5 Global analysis, analysis on manifolds (58-XX) 5 Computer science (68-XX) 4 History and biography (01-XX) 4 Numerical analysis (65-XX) 3 Differential geometry (53-XX) 3 Optics, electromagnetic theory (78-XX) 2 Approximations and expansions (41-XX) 2 General topology (54-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 Topological groups, Lie groups (22-XX) 1 Real functions (26-XX) 1 Measure and integration (28-XX) 1 Functions of a complex variable (30-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Functional analysis (46-XX) 1 Convex and discrete geometry (52-XX) 1 Statistics (62-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Information and communication theory, circuits (94-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 185 Publications have been cited 8,122 times in 6,570 Documents Cited by ▼ Year ▼ Nonlinear oscillations, dynamical systems, and bifurcations of vector fields. Zbl 0515.34001 Guckenheimer, John; Holmes, Philip 3,928 1983 Turbulence, coherent structures, dynamical systems and symmetry. Zbl 0890.76001 Holmes, Philip; Lumley, John L.; Berkooz, Gal 388 1996 The dynamics of coherent structures in the wall region of a turbulent layer. Zbl 0643.76066 Aubry, Nadine; Holmes, Philip; Lumley, John L.; Stone, Emily 275 1988 Turbulence, coherent structures, dynamical systems and symmetry. 2nd ed. Zbl 1251.76001 Holmes, Philip; Lumley, John L.; Berkooz, Gahl; Rowley, Clarence W. 175 2012 A periodically forced piecewise linear oscillator. Zbl 0561.70022 Shaw, S. W.; Holmes, P. J. 155 1983 On the phase reduction and response dynamics of neural oscillator population. Zbl 1054.92006 Brown, Eric; Moehlis, Jeff; Holmes, Philip 123 2004 A nonlinear oscillator with a strange attractor. Zbl 0423.34049 Holmes, P. 122 1979 Heteroclinic cycles and modulated travelling waves in systems with 0(2) symmetry. Zbl 0634.34027 Armbruster, Dieter; Guckenheimer, John; Holmes, Philip 95 1988 Structurally stable heteroclinic cycles. Zbl 0645.58022 Guckenheimer, John; Holmes, Philip 89 1988 A magnetoelastic strange attractor. Zbl 0405.73082 Moon, F. C.; Holmes, P. J. 80 1979 A partial differential equation with infinitely many periodic orbits: Chaotic oscillations of a forced beam. Zbl 0507.58031 Holmes, Philip; Marsden, Jerrold 78 1981 Turbulence, coherent structures, dynamical systems and symmetry. Zbl 0923.76002 Holmes, Philip; Lumley, John L.; Berkooz, Gal 78 1998 Horseshoes in perturbations of Hamiltonian systems with two degrees of freedom. Zbl 0489.58013 Holmes, Philip J.; Marsden, Jerrold E. 76 1982 The dynamics of repeated impacts with a sinusoidally vibrating table. Zbl 0518.73015 Holmes, P. J. 71 1982 Melnikov’s method and Arnold diffusion for perturbations of integrable Hamiltonian systems. Zbl 0497.70025 Holmes, Philip J.; Marsden, Jerrold E. 70 1982 Strong NLS soliton-defect interactions. Zbl 1061.35132 Goodman, Roy H.; Holmes, Philip J.; Weinstein, Michael I. 64 2004 Kuramoto-Sivashinsky dynamics on the center-unstable manifold. Zbl 0687.34036 Armbruster, Dieter; Guckenheimer, John; Holmes, Philip 60 1989 Horseshoes and Arnold diffusion for Hamiltonian systems and Lie groups. Zbl 0488.70006 Holmes, Philip J.; Marsden, Jerrold E. 60 1983 Knots and links in three-dimensional flows. Zbl 0869.58044 Ghrist, Robert W.; Holmes, Philip J.; Sullivan, Michael C. 60 1997 The nature of the coupling between segmental oscillators of the lamprey spinal generator for locomotion: a mathematical model. Zbl 0476.92003 Cohen, Avis H.; Holmes, Philip J.; Rand, Richard H. 55 1982 Averaging and chaotic motions in forced oscillations. Zbl 0472.70024 Holmes, Philip J. 54 1980 The dynamics of legged locomotion: Models, analyses, and challenges. Zbl 1100.34002 Holmes, Philip; Full, Robert J.; Koditschek, Dan; Guckenheimer, John 54 2006 Cascades of homoclinic orbits to, and chaos near, a Hamiltonian saddle- center. Zbl 0749.58022 Mielke, A.; Holmes, P.; O’Reilly, O. 54 1992 Random perturbations of heteroclinic attractors. Zbl 0702.58038 Stone, Emily; Holmes, Philip 51 1990 Global existence theory for a generalized Ginzburg-Landau equation. Zbl 0783.35070 Duan, Jinqiao; Holmes, Philip; Titi, Edriss S. 50 1992 Bifurcation of periodic motions in two weakly coupled van der Pol oscillators. Zbl 0447.70028 Rand, R. H.; Holmes, P. J. 50 1980 Bifurcations to divergence and flutter in flow-induced oscillations: a finite dimensional analysis. Zbl 0363.73059 Holmes, P. J. 49 1977 Phase portraits and bifurcations of the non-linear oscillator: \(x''+(\alpha+\gamma x^ 2)x'+\beta x+\delta x^ 3=0\). Zbl 0453.70015 Holmes, P.; Rand, D. 46 1980 Regularity, approximation and asymptotic dynamics for a generalized Ginzburg-Landau equation. Zbl 0808.35133 Duan, Jinqiao; Titi, Edriss S.; Holmes, Philip 45 1993 On the dynamics of fine structure. Zbl 0791.35030 Ball, J. M.; Holmes, P. J.; James, R. D.; Pego, R. L.; Swart, P. J. 41 1991 Bifurcation to divergence and flutter in flow-induced oscillations: An infinite dimensional analysis. Zbl 0385.93028 Holmes, Philip; Marsden, Jerrold 39 1978 Energy minimization and the formation of microstructure in dynamic anti- plane shear. Zbl 0786.73066 Swart, Pieter J.; Holmes, Philip J. 37 1992 On the relation between low-dimensional models and the dynamics of coherent structures in the turbulent wall layer. Zbl 0782.76048 Berkooz, Gal; Holmes, Philip; Lumley, J. L. 35 1993 On the Cauchy problem of a generalized Ginzburg-Landau equation. Zbl 0833.35067 Duan, Jinqiao; Holmes, Philip 33 1994 Bifurcations of one- and two-dimensional maps. Zbl 0556.58023 Holmes, P.; Whitley, D. 32 1984 Nonlinear propagation of light in one-dimensional periodic structures. Zbl 1005.78011 Goodman, R. H.; Weinstein, M. I.; Holmes, P. J. 32 2001 Second order averaging and bifurcations to subharmonics in Duffing’s equation. Zbl 0478.73028 Holmes, C.; Holmes, P. 28 1981 Homoclinic orbits, subharmonics and global bifurcations in forced oscillations. Zbl 0532.58019 Greenspan, B. D.; Holmes, P. J. 28 1983 Interaction of sine-Gordon kinks with defects: Phase space transport in a two-mode model. Zbl 0985.35074 Goodman, Roy H.; Holmes, Philip J.; Weinstein, Michael I. 28 2002 Knotted periodic orbits in suspensions of Smale’s horseshoe: torus knots and bifurcation sequences. Zbl 0593.58027 Holmes, Philip; Williams, R. F. 28 1985 Stable and random motions in dynamical systems. With special emphasis on celestial mechanics. With a new foreword by Philip J. Holmes. 3rd pbk-ed. 3rd pbk-ed. Zbl 0991.70002 Moser, Jürgen 27 2001 Periodic orbits in slowly varying oscillators. Zbl 0619.34041 Wiggins, Stephen; Holmes, Philip 27 1987 Spatially complex equilibria of buckled rods. Zbl 0655.73029 Mielke, Alexander; Holmes, Philip 26 1988 A periodically forced impact oscillator with large dissipation. Zbl 0539.70032 Shaw, S. W.; Holmes, P. J. 26 1983 Celestial encounters. The origins of chaos and stability. Zbl 0944.37001 Diacu, Florin; Holmes, Philip 25 1996 Homoclinic orbits in slowly varying oscillators. Zbl 0622.34041 Wiggins, Stephen; Holmes, Philip 25 1987 Repeated resonance and homoclinic bifurcation in a periodically forced family of oscillators. Zbl 0547.34028 Greenspan, Bernie; Holmes, Philip 24 1984 The dynamics of choice among multiple alternatives. Zbl 1139.91028 McMillen, Tyler; Holmes, Philip 24 2006 Bifurcations of the forced van der Pol oscillator. Zbl 0375.34031 Holmes, P. J.; Rand, D. A. 24 1978 Exponentially small splittings of separatrices with applications of KAM theory and degenerate bifurcations. Zbl 0685.70017 Holmes, Philip; Marsden, Jerrold; Scheurle, Jürgen 23 1988 Globally coupled oscillator networks. Zbl 1132.92316 Brown, Eric; Holmes, Philip; Moehlis, Jeff 23 2003 Low-dimensional modelling of turbulence using the proper orthogonal decomposition: A tutorial. Zbl 1094.76024 Smith, Troy R.; Moehlis, Jeff; Holmes, Philip 23 2005 On a Painlevé-type boundary-value problem. Zbl 0552.34023 Holmes, Philip; Spence, David 21 1984 Constrained Euler buckling: An interplay of computation and analysis. Zbl 0949.74023 Holmes, Philip; Domokos, Gábor; Schmitt, John; Szeberényi, Imre 21 1999 Fronts, domain walls and pulses in a generalized Ginzburg-Landau equation. Zbl 0820.58053 Duan, Jinqiao; Holmes, Philip 21 1995 Constrained Euler buckling. Zbl 0876.34047 Domokos, G.; Holmes, P.; Royce, B. 21 1997 Nonlinear stability of axisymmetric swirling flows. Zbl 0658.76044 Szeri, A.; Holmes, P. 19 1988 Chaotic motions in a weakly nonlinear model for surface waves. Zbl 0602.76015 Holmes, Philip 19 1986 Dynamics of the Kirchhoff equations. I: Coincident centers of gravity and buoyancy. Zbl 1194.70009 Holmes, Philip; Jenkins, Jeffrey; Leonard, Naomi Ehrich 19 1998 Spatial structure of time-periodic solutions of the Ginzburg-Landau equation. Zbl 0618.35003 Holmes, Philip 18 1986 The limited effectiveness of normal forms: A critical review and extension of local bifurcation studies of the Brusselator PDE. Zbl 0893.34027 Wittenberg, Ralf W.; Holmes, Philip 18 1997 Some remarks on chaotic particle paths in time-periodic, three- dimensional swirling flows. Zbl 0521.76049 Holmes, Philip 17 1984 The existence of transverse homoclinic points in the Sitnikov problem. Zbl 0815.34032 Dankowicz, Harry; Holmes, Philip 17 1995 Simple neural networks that optimize decisions. Zbl 1069.92004 Brown, Eric; Gao, Juan; Holmes, Philip; Bogacz, Rafal; Gilzenrat, Mark; Cohen, Jonathan D. 17 2005 Mechanical models for insect locomotion: Dynamics and stability in the horizontal plane. I: Theory. Zbl 1033.92005 Schmitt, John; Holmes, Philip 17 2000 The bifurcations of Duffing’s equation: An application of catastrophe theory. Zbl 0337.34049 Holmes, P. J.; Rand, D. A. 17 1976 Minimal models of bursting neurons: How multiple currents, conductances, and timescales affect bifurcation diagrams. Zbl 1090.34039 Ghigliazza, R. M.; Holmes, P. 16 2004 Low-dimensional models for turbulent plane Couette flow in a minimal flow unit. Zbl 1108.76031 Smith, T. R.; Moehlis, J.; Holmes, P. 15 2005 Rapid decision threshold modulation by reward rate in a neural network. Zbl 1103.68726 Simen, Patrick; Cohen, Jonathan D.; Holmes, Philip 15 2006 Knotted periodic orbits in suspensions of Smale’s horseshoe: period multiplying and cabled knots. Zbl 0623.58014 Holmes, Philip 15 1986 A phase-reduced neuro-mechanical model for insect locomotion: feed-forward stability and proprioceptive feedback. Zbl 1211.93099 Proctor, J.; Kukillaya, R. P.; Holmes, P. 14 2010 Noise induced intermittency in a model of a turbulent boundary layer. Zbl 0687.76055 Stone, Emily; Holmes, Philip 14 1989 A simply stabilized running model. Zbl 1088.34517 Ghigliazza, R. M.; Altendorfer, R.; Holmes, P.; Koditschek, D. 14 2003 Models for turbulent plane Couette flow using the proper orthogonal decomposition. Zbl 1185.76261 Moehlis, J.; Smith, T. R.; Holmes, P.; Faisst, H. 13 2002 On the attracting set for Duffing’s equation. II: A geometrical model for moderate force and damping. Zbl 0574.58024 Holmes, Philip; Whitley, David 13 1983 Josephson’s junction, annulus maps, Birkhoff attractors, horseshoes and rotation sets. Zbl 0582.58020 Hockett, Kevin; Holmes, Philip 13 1986 The existence of arbitrarily many distinct periodic orbits in a two degree of freedom Hamiltonian system. Zbl 0595.58036 Veerman, Peter; Holmes, Philip 13 1985 Intermittent dynamics in simple models of the turbulent wall layer. Zbl 0729.76040 Berkooz, Gal; Holmes, Philip; Lumley, J. L. 13 1991 Bifurcation from \(O(2)\) symmetric heteroclinic cycles with three interacting modes. Zbl 0737.58038 Campbell, Sue Ann; Holmes, Philip 13 1991 An ODE whose solutions contain all knots and links. Zbl 0878.34038 Ghrist, Robert W.; Holmes, Philip J. 13 1996 A hexapedal jointed-leg model for insect locomotion in the horizontal plane. Zbl 1248.92003 Kukillaya, Raghavendra P.; Holmes, Philip J. 12 2007 Mechanical models for insect locomotion: Dynamics and stability in the horizontal plane. II: Application. Zbl 1039.92006 Schmitt, John; Holmes, Philip 12 2000 Pipes supported at both ends cannot flutter. Zbl 0386.73056 Holmes, P. J. 12 1978 Center manifolds, normal forms and bifurcations of vector fields with application to coupling between periodic and steady motions. Zbl 1194.37075 Holmes, Philip J. 12 1981 A minimal model of a central pattern generator and motoneurons for insect locomotion. Zbl 1090.34040 Ghigliazza, R. M.; Holmes, P. 11 2004 A strange family of three-dimensional vector fields near a degenerate singularity. Zbl 0421.58016 Holmes, Philip J. 11 1980 Dynamics and stability of insect locomotion: a hexapedal model for horizontal plane motions. Zbl 1082.92010 Seipel, Justin E.; Holmes, Philip J.; Full, Robert J. 11 2004 An elastic rod model for anguilliform swimming. Zbl 1113.92005 McMillan, T.; Holmes, P. 10 2006 A simple model for clock-actuated legged locomotion. Zbl 1229.70028 Seipel, J.; Holmes, P. 10 2007 Homoclinic explosions and implosions. Zbl 0881.58044 Doelman, Arjen; Holmes, Philip 10 1996 Dynamics and stability of legged locomotion in the horizontal plane: a test case using insects. Zbl 1068.92004 Schmitt, J.; Garcia, M.; Razo, R. C.; Holmes, P.; Full, R. J. 10 2002 Modeling a simple choice task: Stochastic dynamics of mutually inhibitory neural groups. Zbl 1060.92019 Brown, Eric; Holmes, Philip 9 2001 Euler’s problem, Euler’s method, and the standard map; or, the discrete charm of buckling. Zbl 0797.34041 Domokos, G.; Holmes, P. 9 1993 Proof of non-integrability for the Hénon-Heiles Hamiltonian near an exceptional integrable case. Zbl 1194.37128 Holmes, Philip 9 1982 On linearly coupled relaxation oscillations. Zbl 0565.70025 Bélair, Jacques; Holmes, Philip 8 1984 Mechanical models for insect locomotion: Stability and parameter studies. Zbl 1059.70006 Schmitt, John; Holmes, Philip 8 2001 Ninety plus thirty years of nonlinear dynamics: less is more and more is different. Zbl 1092.37500 Holmes, Philip 8 2005 The effect of modeled drag reduction on the wall region. Zbl 0708.76072 Aubry, N.; Lumley, J. L.; Holmes, P. 8 1990 Motions and stability of a piecewise holonomic system: The discrete Chaplygin sleigh. Zbl 1020.70007 Coleman, M. J.; Holmes, P. 8 1999 On the dynamics of cranes, or spherical pendula with moving supports. Zbl 1346.37069 Ghigliazza, R. M.; Holmes, P. 7 2002 Some elements for a history of the dynamical systems theory. Zbl 1462.37002 Letellier, Christophe; Abraham, Ralph; Shepelyansky, Dima L.; Rössler, Otto E.; Holmes, Philip; Lozi, René; Glass, Leon; Pikovsky, Arkady; Olsen, Lars F.; Tsuda, Ichiro; Grebogi, Celso; Parlitz, Ulrich; Gilmore, Robert; Pecora, Louis M.; Carroll, Thomas L. 3 2021 Heterogeneous inputs to central pattern generators can shape insect gaits. Zbl 1425.92036 Aminzare, Zahra; Holmes, Philip 2 2019 Gait transitions in a phase oscillator model of an insect central pattern generator. Zbl 1385.92007 Aminzare, Zahra; Srivastava, Vaibhav; Holmes, Philip 6 2018 Explicit moments of decision times for single- and double-threshold drift-diffusion processes. Zbl 1396.91627 Srivastava, V.; Holmes, P.; Simen, P. 3 2016 A genealogy of convex solids via local and global bifurcations of gradient vector fields. Zbl 1359.52005 Domokos, Gábor; Holmes, Philip; Lángi, Zsolt 3 2016 Some joys and trials of mathematical neuroscience. Zbl 1293.92006 Holmes, Philip 2 2014 Turbulence, coherent structures, dynamical systems and symmetry. 2nd ed. Zbl 1251.76001 Holmes, Philip; Lumley, John L.; Berkooz, Gahl; Rowley, Clarence W. 175 2012 Neural dynamics, bifurcations, and firing rates in a quadratic integrate-and-fire model with a recovery variable. I: Deterministic behavior. Zbl 1311.92051 Shlizerman, Eli; Holmes, Philip 6 2012 Dimension reduction and dynamics of a spiking neural network model for decision making under neuromodulation. Zbl 1217.34079 Eckhoff, Philip; Wong-Lin, Kongfatt; Holmes, Philip 3 2011 A phase-reduced neuro-mechanical model for insect locomotion: feed-forward stability and proprioceptive feedback. Zbl 1211.93099 Proctor, J.; Kukillaya, R. P.; Holmes, P. 14 2010 Reflexes and preflexes: on the role of sensory feedback on rhythmic patterns in insect locomotion. Zbl 1266.92037 Proctor, J.; Holmes, P. 6 2010 Robust versus optimal strategies for two-alternative forced choice tasks. Zbl 1204.91043 Zacksenhouse, M.; Bogacz, R.; Holmes, P. 1 2010 A model for insect locomotion in the horizontal plane: feedforward activation of fast muscles, stability, and robustness. Zbl 1403.92015 Kukillaya, Raghavendra P.; Holmes, Philip 6 2009 A comparison of bounded diffusion models for choice in time controlled tasks. Zbl 1176.60075 Zhang, Jiaxiang; Bogacz, Rafal; Holmes, Philip 5 2009 Sequential effects in two-choice reaction time tasks: decomposition and synthesis of mechanisms. Zbl 1402.92086 Gao, Juan; Wong-Lin, KongFatt; Holmes, Philip; Simen, Patrick; Cohen, Jonathan D. 4 2009 Dynamical analysis of Bayesian inference models for the Eriksen task. Zbl 1183.68487 Liu, Yuan Sophie; Yu, Angela; Holmes, Philip 3 2009 Closed-form approximations of first-passage distributions for a stochastic decision-making model. Zbl 1186.91061 Broderick, Tamara; Wong-Lin, Kong Fatt; Holmes, Philip 2 2009 Time-varying perturbations can distinguish among integrate-to-threshold models for perceptual decision making in reaction time tasks. Zbl 1168.91515 Zhou, Xiang; Wong-Lin, Kongfatt; Holmes, Philip 2 2009 How well can spring-mass-like telescoping leg models fit multi-pedal sagittal-plane locomotion data? Zbl 1400.92052 Srinivasan, Manoj; Holmes, Philip 7 2008 A neural network model of the Eriksen task: reduction, analysis, and data fitting. Zbl 1146.68421 Liu, Yuan Sophie; Holmes, Philip; Cohen, Jonathan D. 4 2008 Steering by transient destabilization in piecewise-holonomic models of legged locomotion. Zbl 1229.70018 Proctor, J.; Holmes, P. 2 2008 On synchronization and traveling waves in chains of relaxation oscillators with an application to Lamprey CPG. Zbl 1167.34347 Várkonyi, Péter L.; Holmes, Philip 1 2008 A hexapedal jointed-leg model for insect locomotion in the horizontal plane. Zbl 1248.92003 Kukillaya, Raghavendra P.; Holmes, Philip J. 12 2007 A simple model for clock-actuated legged locomotion. Zbl 1229.70028 Seipel, J.; Holmes, P. 10 2007 The dynamics of legged locomotion: Models, analyses, and challenges. Zbl 1100.34002 Holmes, Philip; Full, Robert J.; Koditschek, Dan; Guckenheimer, John 54 2006 The dynamics of choice among multiple alternatives. Zbl 1139.91028 McMillen, Tyler; Holmes, Philip 24 2006 Rapid decision threshold modulation by reward rate in a neural network. Zbl 1103.68726 Simen, Patrick; Cohen, Jonathan D.; Holmes, Philip 15 2006 An elastic rod model for anguilliform swimming. Zbl 1113.92005 McMillan, T.; Holmes, P. 10 2006 Low-dimensional modelling of turbulence using the proper orthogonal decomposition: A tutorial. Zbl 1094.76024 Smith, Troy R.; Moehlis, Jeff; Holmes, Philip 23 2005 Simple neural networks that optimize decisions. Zbl 1069.92004 Brown, Eric; Gao, Juan; Holmes, Philip; Bogacz, Rafal; Gilzenrat, Mark; Cohen, Jonathan D. 17 2005 Low-dimensional models for turbulent plane Couette flow in a minimal flow unit. Zbl 1108.76031 Smith, T. R.; Moehlis, J.; Holmes, P. 15 2005 Ninety plus thirty years of nonlinear dynamics: less is more and more is different. Zbl 1092.37500 Holmes, Philip 8 2005 A simply stabilized running model. Zbl 1074.70005 Ghigliazza, R. M.; Altendorfer, R.; Holmes, P.; Koditschek, D. 4 2005 Towards a neuromechanical model for insect locomotion: hybrid dynamical systems. Zbl 1084.34050 Ghigliazza, R. M.; Holmes, P. 3 2005 Heteroclinic cycles and periodic orbits for the O(2)-equivariant 0:1:2 mode interaction. Zbl 1099.37044 Smith, T. R.; Moehlis, J.; Holmes, P. 2 2005 On the phase reduction and response dynamics of neural oscillator population. Zbl 1054.92006 Brown, Eric; Moehlis, Jeff; Holmes, Philip 123 2004 Strong NLS soliton-defect interactions. Zbl 1061.35132 Goodman, Roy H.; Holmes, Philip J.; Weinstein, Michael I. 64 2004 Minimal models of bursting neurons: How multiple currents, conductances, and timescales affect bifurcation diagrams. Zbl 1090.34039 Ghigliazza, R. M.; Holmes, P. 16 2004 A minimal model of a central pattern generator and motoneurons for insect locomotion. Zbl 1090.34040 Ghigliazza, R. M.; Holmes, P. 11 2004 Dynamics and stability of insect locomotion: a hexapedal model for horizontal plane motions. Zbl 1082.92010 Seipel, Justin E.; Holmes, Philip J.; Full, Robert J. 11 2004 Globally coupled oscillator networks. Zbl 1132.92316 Brown, Eric; Holmes, Philip; Moehlis, Jeff 23 2003 A simply stabilized running model. Zbl 1088.34517 Ghigliazza, R. M.; Altendorfer, R.; Holmes, P.; Koditschek, D. 14 2003 Travelling wave solutions of the degenerate Kolmogorov-Petrovski-Piskunov equation. Zbl 1060.35052 Medvedev, G. S.; Ono, K.; Holmes, P. J. 6 2003 On nonlinear boundary-value problems: Ghosts, parasites and discretizations. Zbl 1069.34020 Domokos, G.; Holmes, P. 5 2003 Mechanical models for insect locomotion: active muscles and energy losses. Zbl 1105.92307 Schmitt, John; Holmes, Philip 3 2003 Buckling in response to applied heat sources. Zbl 1083.74021 Cisternas, Jaime; Holmes, Philip; Kevrekidis, Ioannis G. 2 2003 Interaction of sine-Gordon kinks with defects: Phase space transport in a two-mode model. Zbl 0985.35074 Goodman, Roy H.; Holmes, Philip J.; Weinstein, Michael I. 28 2002 Models for turbulent plane Couette flow using the proper orthogonal decomposition. Zbl 1185.76261 Moehlis, J.; Smith, T. R.; Holmes, P.; Faisst, H. 13 2002 Dynamics and stability of legged locomotion in the horizontal plane: a test case using insects. Zbl 1068.92004 Schmitt, J.; Garcia, M.; Razo, R. C.; Holmes, P.; Full, R. J. 10 2002 On the dynamics of cranes, or spherical pendula with moving supports. Zbl 1346.37069 Ghigliazza, R. M.; Holmes, P. 7 2002 Geometry, mechanics, and dynamics. Volume in honor of the 60th birthday of J. E. Marsden. Zbl 0993.00007 2 2002 Buckling of extensible thermoelastic rods. Zbl 1027.74025 Cisternas, J.; Holmes, P. 1 2002 Nonlinear propagation of light in one-dimensional periodic structures. Zbl 1005.78011 Goodman, R. H.; Weinstein, M. I.; Holmes, P. J. 32 2001 Stable and random motions in dynamical systems. With special emphasis on celestial mechanics. With a new foreword by Philip J. Holmes. 3rd pbk-ed. 3rd pbk-ed. Zbl 0991.70002 Moser, Jürgen 27 2001 Modeling a simple choice task: Stochastic dynamics of mutually inhibitory neural groups. Zbl 1060.92019 Brown, Eric; Holmes, Philip 9 2001 Mechanical models for insect locomotion: Stability and parameter studies. Zbl 1059.70006 Schmitt, John; Holmes, Philip 8 2001 Homoclinic orbits and chaos in three- and four-dimensional flows. Zbl 1004.37013 Holmes, Philip; Doelman, Arjen; Hek, Geertje; Domokos, Gábor 3 2001 Low-dimensional models with varying parameters: A model problem and flow through a diffuser with variable angle. Zbl 1020.76041 Smith, Troy; Holmes, Philip 1 2001 On the global dynamics of Kirchhoff’s equations: Rigid body models for underwater vehicles. Zbl 1015.37043 Hanßmann, Heinz; Holmes, Philip 1 2001 Mechanical models for insect locomotion: Dynamics and stability in the horizontal plane. I: Theory. Zbl 1033.92005 Schmitt, John; Holmes, Philip 17 2000 Mechanical models for insect locomotion: Dynamics and stability in the horizontal plane. II: Application. Zbl 1039.92006 Schmitt, John; Holmes, Philip 12 2000 Euler buckling in a potential field. Zbl 1139.74415 Holmes, P.; Domokos, G.; Hek, G. 7 2000 Constrained Euler buckling: An interplay of computation and analysis. Zbl 0949.74023 Holmes, Philip; Domokos, Gábor; Schmitt, John; Szeberényi, Imre 21 1999 Motions and stability of a piecewise holonomic system: The discrete Chaplygin sleigh. Zbl 1020.70007 Coleman, M. J.; Holmes, P. 8 1999 Constrained Euler buckling: Line contact solutions. Zbl 0983.74024 Holmes, Philip; Schmitt, John; Domokos, Gabor 1 1999 Dynamics and bifurcations of a planar map modeling dispersion managed breathers. Zbl 0936.34030 Holmes, Philip; Kutz, J. Nathan 1 1999 Turbulence, coherent structures, dynamical systems and symmetry. Zbl 0923.76002 Holmes, Philip; Lumley, John L.; Berkooz, Gal 78 1998 Dynamics of the Kirchhoff equations. I: Coincident centers of gravity and buoyancy. Zbl 1194.70009 Holmes, Philip; Jenkins, Jeffrey; Leonard, Naomi Ehrich 19 1998 Simple models for excitable and oscillatory neural networks. Zbl 0908.92013 Taylor, David; Holmes, Philip 7 1998 Homoclinic saddle-node bifurcations and subshifts in a three-dimensional flow. Zbl 0930.37026 Hek, Geertje; Doelman, Arjen; Holmes, Philip 4 1998 Global existence and uniqueness for an optical fibre laser model. Zbl 0913.35018 Mielke, Alexander; Holmes, Philip; Kutz, J. Nathan 1 1998 Knots and links in three-dimensional flows. Zbl 0869.58044 Ghrist, Robert W.; Holmes, Philip J.; Sullivan, Michael C. 60 1997 Constrained Euler buckling. Zbl 0876.34047 Domokos, G.; Holmes, P.; Royce, B. 21 1997 The limited effectiveness of normal forms: A critical review and extension of local bifurcation studies of the Brusselator PDE. Zbl 0893.34027 Wittenberg, Ralf W.; Holmes, Philip 18 1997 Suppression of bursting. Zbl 0868.93057 Coller, B. D.; Holmes, Philip 5 1997 Erratum: ”Interaction of adjacent bursts in the wall region” [Phys. Fluids 6 (1994), no. 2, part 2, 954–961]. Zbl 1185.76746 Coller, B. D.; Holmes, P.; Lumley, John 1 1997 Turbulence, coherent structures, dynamical systems and symmetry. Zbl 0890.76001 Holmes, Philip; Lumley, John L.; Berkooz, Gal 388 1996 Celestial encounters. The origins of chaos and stability. Zbl 0944.37001 Diacu, Florin; Holmes, Philip 25 1996 An ODE whose solutions contain all knots and links. Zbl 0878.34038 Ghrist, Robert W.; Holmes, Philip J. 13 1996 Homoclinic explosions and implosions. Zbl 0881.58044 Doelman, Arjen; Holmes, Philip 10 1996 On a dynamical model for phase transformation in nonlinear elasticity. Zbl 0876.73015 Kalies, W. D.; Holmes, P. J. 5 1996 Local models of spatio-temporally complex fields. Zbl 0885.35115 Dankowicz, Harry; Holmes, Philip; Berkooz, Gal; Elezgaray, Juan 4 1996 Fronts, domain walls and pulses in a generalized Ginzburg-Landau equation. Zbl 0820.58053 Duan, Jinqiao; Holmes, Philip 21 1995 The existence of transverse homoclinic points in the Sitnikov problem. Zbl 0815.34032 Dankowicz, Harry; Holmes, Philip 17 1995 Wavelet projections of the Kuramoto-Sivashinsky equation. I: Heteroclinic cycles and modulated traveling waves for short systems. Zbl 0890.58086 Myers, Mark; Holmes, Philip; Elezgaray, Juan; Berkooz, Gal 3 1995 On the Cauchy problem of a generalized Ginzburg-Landau equation. Zbl 0833.35067 Duan, Jinqiao; Holmes, Philip 33 1994 Control of noisy heteroclinic cycles. Zbl 0816.76037 Coller, B. D.; Holmes, Philip; Lumley, John L. 7 1994 Interaction of adjacent bursts in the wall region. Zbl 0830.76040 Coller, B. D.; Holmes, P.; Lumley, J. L. 2 1994 Knotting within the gluing bifurcation. Zbl 0864.58045 Holmes, P.; Ghrist, R. 2 1994 The proper orthogonal decomposition, wavelets and modal approaches to the dynamics of coherent structures. Zbl 0823.76036 Berkooz, Gal; Elezgaray, Juan; Holmes, Philip; Lumley, John; Poje, Andrew 1 1994 Regularity, approximation and asymptotic dynamics for a generalized Ginzburg-Landau equation. Zbl 0808.35133 Duan, Jinqiao; Titi, Edriss S.; Holmes, Philip 45 1993 On the relation between low-dimensional models and the dynamics of coherent structures in the turbulent wall layer. Zbl 0782.76048 Berkooz, Gal; Holmes, Philip; Lumley, J. L. 35 1993 Euler’s problem, Euler’s method, and the standard map; or, the discrete charm of buckling. Zbl 0797.34041 Domokos, G.; Holmes, P. 9 1993 Knots and orbit genealogies in three dimensional flows. Zbl 0803.58047 Ghrist, Robert; Holmes, Philip 4 1993 Wavelet analysis of the motion of coherent structures. Zbl 0899.76236 Elezgaray, J.; Berkooz, G.; Holmes, P. 3 1993 Reduction, stability, instability and bifurcation in rotationally symmetric Hamiltonian systems. Zbl 0782.70015 Zombro, Brett; Holmes, Philip 2 1993 Symmetries, heteroclinic cycles and intermittency in fluid flow. Zbl 0788.76008 Holmes, Philip 1 1993 On non-inflectional solutions of non-uniform elasticae. Zbl 0793.73036 Domokos, Gábor; Holmes, Philip 1 1993 Cascades of homoclinic orbits to, and chaos near, a Hamiltonian saddle- center. Zbl 0749.58022 Mielke, A.; Holmes, P.; O’Reilly, O. 54 1992 Global existence theory for a generalized Ginzburg-Landau equation. Zbl 0783.35070 Duan, Jinqiao; Holmes, Philip; Titi, Edriss S. 50 1992 ...and 85 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 8,438 Authors 76 Holmes, Philip J. 53 Li, Jibin 50 Llibre, Jaume 47 Luo, Zhendong 37 Zhang, Weinian 35 Yagasaki, Kazuyuki 32 Ashwin, Peter 29 Xu, Wei 29 Yu, Pei 28 Algaba, Antonio 28 Jing, Zhujun 28 Marsden, Jerrold Eldon 27 Iliescu, Traian 27 Rodríguez-Luis, Alejandro J. 25 Moehlis, Jeff 23 Brunton, Steven L. 23 Chen, Guanrong 23 Fečkan, Michal 23 Rand, Richard H. 22 Haller, George 22 Knobloch, Edgar 22 Kühn, Christian 22 Noack, Bernd R. 22 Zhang, Wei 21 Stewart, Ian Nicholas 21 Wilson, Dan D. 20 Jiang, Weihua 20 Krauskopf, Bernd 20 Kutz, J. Nathan 20 Luo, Albert C. J. 19 Balasuriya, Sanjeeva 19 Champneys, Alan R. 19 Volkwein, Stefan 18 Buonomo, Bruno 18 Feichtinger, Gustav 18 Guo, Boling 18 Han, Maoan 18 Xie, Jianhua 17 Duan, Jinqiao 17 Lu, Qishao 17 M-Seara, Tere 16 Din, Qamar 16 Golubitsky, Martin A. 16 Guckenheimer, John M. 16 Kevrekidis, Ioannis George 15 Aubry, Nadine 15 Bi, Qinsheng 15 Campbell, Sue Ann 15 Doelman, Arjen 15 Piqueira, José Roberto Castilho 15 Postlethwaite, Claire M. 15 Shen, Jianwei 15 Wiercigroch, Marian 14 Broer, Henk W. 14 Chen, Hebai 14 Gardini, Laura 14 Guo, Shangjiang 14 Kuznetsov, Yuri Alexandrovich 14 Liu, Qian 14 Merino, Manuel 14 Rega, Giuseppe 14 Rodrigues, Alexandre A. P. 14 Rowley, Clarence Worth 14 Rozza, Gianluigi 14 Wang, Zhu 14 Wiggins, Stephen R. 14 Yang, Qigui 14 Yorke, James Alan 13 Awrejcewicz, Jan 13 Battelli, Flaviano 13 Chen, Yushu 13 Lumley, John Leask 13 Mezić, Igor 13 Niu, Ben 13 Osinga, Hinke Maria 13 Wei, Junjie 12 Freire Macías, Emilio 12 Gamero, Estanislao 12 Grebogi, Celso 12 Huseyin, Koncay 12 Navon, Ionel Michael 12 Podvin, Bérengère 12 Rom-Kedar, Vered 12 Sapsis, Themistoklis P. 12 Shu, Ji 12 Tang, Yilei 11 Akhmet, Marat Ubaydulla 11 Bishop, Steven R. 11 Cao, Qingjie 11 Ermentrout, George Bard 11 Gao, Hongjun 11 Jiang, Guirong 11 Kulikov, Anatoliĭ Nikolaevich 11 Kulikov, Dmitriĭ Anatol’evich 11 Labouriau, Isabel S. 11 Lacitignola, Deborah 11 Lenci, Stefano 11 Palacios, Antonio 11 Proctor, Joshua L. 11 Rucklidge, Alastair M. ...and 8,338 more Authors all top 5 Cited in 536 Serials 564 Physica D 425 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 280 Chaos, Solitons and Fractals 248 Nonlinear Dynamics 193 Journal of Fluid Mechanics 176 Chaos 166 Journal of Differential Equations 152 Communications in Nonlinear Science and Numerical Simulation 127 Applied Mathematics and Computation 105 Journal of Computational Physics 100 SIAM Journal on Applied Dynamical Systems 96 Journal of Nonlinear Science 85 Physics of Fluids 75 Journal of Mathematical Analysis and Applications 72 Journal of Mathematical Biology 72 Physics Letters. 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Fluids 13 Mathematical Biosciences and Engineering 13 The Journal of Mathematical Neuroscience 12 Applicable Analysis 12 Journal of Economic Theory 12 Computational Mechanics 12 SIAM Review ...and 436 more Serials all top 5 Cited in 59 Fields 2,595 Dynamical systems and ergodic theory (37-XX) 2,158 Ordinary differential equations (34-XX) 1,046 Biology and other natural sciences (92-XX) 971 Fluid mechanics (76-XX) 953 Partial differential equations (35-XX) 877 Mechanics of particles and systems (70-XX) 638 Numerical analysis (65-XX) 449 Systems theory; control (93-XX) 429 Mechanics of deformable solids (74-XX) 256 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 165 Probability theory and stochastic processes (60-XX) 145 Computer science (68-XX) 136 Difference and functional equations (39-XX) 132 Statistical mechanics, structure of matter (82-XX) 123 Calculus of variations and optimal control; optimization (49-XX) 90 Information and communication theory, circuits (94-XX) 87 Quantum theory (81-XX) 86 Classical thermodynamics, heat transfer (80-XX) 79 Optics, electromagnetic theory (78-XX) 70 Global analysis, analysis on manifolds (58-XX) 68 Geophysics (86-XX) 67 Manifolds and cell complexes (57-XX) 66 Statistics (62-XX) 54 Operations research, mathematical programming (90-XX) 50 Operator theory (47-XX) 38 Differential geometry (53-XX) 25 Relativity and gravitational theory (83-XX) 23 General topology (54-XX) 21 History and biography (01-XX) 21 Measure and integration (28-XX) 20 Real functions (26-XX) 19 Integral equations (45-XX) 16 Combinatorics (05-XX) 16 Approximations and expansions (41-XX) 15 General and overarching topics; collections (00-XX) 13 Linear and multilinear algebra; matrix theory (15-XX) 12 Astronomy and astrophysics (85-XX) 11 Harmonic analysis on Euclidean spaces (42-XX) 10 Mathematical logic and foundations (03-XX) 9 Functional analysis (46-XX) 8 Special functions (33-XX) 7 Number theory (11-XX) 7 Algebraic topology (55-XX) 6 Algebraic geometry (14-XX) 6 Topological groups, Lie groups (22-XX) 6 Mathematics education (97-XX) 4 Field theory and polynomials (12-XX) 4 Commutative algebra (13-XX) 4 Group theory and generalizations (20-XX) 4 Convex and discrete geometry (52-XX) 3 Functions of a complex variable (30-XX) 3 Several complex variables and analytic spaces (32-XX) 3 Sequences, series, summability (40-XX) 3 Geometry (51-XX) 2 Category theory; homological algebra (18-XX) 2 Integral transforms, operational calculus (44-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Nonassociative rings and algebras (17-XX) 1 Potential theory (31-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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