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Holmes, Philip J.

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Author ID: holmes.philip-j Recent zbMATH articles by "Holmes, Philip J."
Published as: Holmes, P.; Holmes, P. J.; Holmes, Philip; Holmes, Philip J.
Homepage: https://www.princeton.edu/mae/people/faculty/holmes/
External Links: MGP · Math-Net.Ru · Wikidata · dblp · GND
Documents Indexed: 209 Publications since 1976, including 9 Books
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 Brown, Eric N.
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 Koditschek, Dan
3 Kukillaya, Raghavendra P.
3 Mielke, Alexander
3 Rand, David A.
3 Simen, Patrick
3 Swart, Pieter J.
3 Weinstein, Michael I.
3 Whitley, David L.
3 Wiggins, Stephen
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 Shaw, Steven W.
2 Szeri, Andrew J.
2 Titi, Edriss Saleh
2 Veerman, Peter
1 Ball, John M.
1 Ball, Rowena
1 Bélair, Jacques
1 Broderick, Tamara
1 Brunsden, V.
1 Clarkson, B. L.
1 Coleman, Michael J.
1 Cortell, J.
1 Cusumano, Joseph P.
1 Diacu, Florin Nicolae
1 Eckhoff, Philip
1 Faisst, Holger
1 Garcia, Mark Anthony
1 Gilzenrat, Mark S.
1 Greenspan, B. D.
1 Greenspan, Bernie
1 Hammond, Joseph K.
1 Hanßmann, Heinz
1 Harris-Warrick, Ronald M.
1 Hoffman, Kathleen A.
1 Holmes, Catherine A.
1 Ilyashenko, Yulij Sergeevich
1 James, Richard D.
1 Jenkins, Jeffrey
1 Kalies, William D.
1 Kevrekidis, Ioannis George
1 Khibnik, Alexander I.
1 Kiemel, Tim
1 Kistner, A.
1 Lángi, Zsolt
1 Leibovich, Sidney
1 Leonard, Naomi Ehrich
1 Lewis, Donald C.
1 Lin, Yue-Kuhn
1 Mattingly, Jonathan C.
1 McMillan, Thomas
1 McMillen, Tyler
1 Medvedev, Georgi S.
1 Myers, Mark H.
1 Newton, Paul K.
1 Ono, Kinya
1 Pego, Robert L.
1 Razo, R. C.
1 Rowley, Clarence W.
1 Scheurle, Jürgen
...and 23 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 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 IMA Journal of Applied Mathematics
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 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 Nonlinear Analysis. Theory, Methods & Applications
1 Cambridge Monographs on Mechanics

Publications by Year

Citations contained in zbMATH

182 Publications have been cited 7,513 times in 6,010 Documents Cited by Year
Nonlinear oscillations, dynamical systems, and bifurcations of vector fields. Zbl 0515.34001
Guckenheimer, John; Holmes, Philip
1983
Turbulence, coherent structures, dynamical systems and symmetry. Zbl 0890.76001
Holmes, Philip; Lumley, John L.; Berkooz, Gal
320
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
247
1988
A periodically forced piecewise linear oscillator. Zbl 0561.70022
Shaw, S. W.; Holmes, P. J.
131
1983
A nonlinear oscillator with a strange attractor. Zbl 0423.34049
Holmes, P.
110
1979
Turbulence, coherent structures, dynamical systems and symmetry. 2nd ed. Zbl 1251.76001
Holmes, Philip; Lumley, John L.; Berkooz, Gahl; Rowley, Clarence W.
97
2012
On the phase reduction and response dynamics of neural oscillator population. Zbl 1054.92006
Brown, Eric; Moehlis, Jeff; Holmes, Philip
97
2004
Heteroclinic cycles and modulated travelling waves in systems with 0(2) symmetry. Zbl 0634.34027
Armbruster, Dieter; Guckenheimer, John; Holmes, Philip
90
1988
A partial differential equation with infinitely many periodic orbits: Chaotic oscillations of a forced beam. Zbl 0507.58031
Holmes, Philip; Marsden, Jerrold
76
1981
Structurally stable heteroclinic cycles. Zbl 0645.58022
Guckenheimer, John; Holmes, Philip
75
1988
Horseshoes in perturbations of Hamiltonian systems with two degrees of freedom. Zbl 0489.58013
Holmes, Philip J.; Marsden, Jerrold E.
73
1982
Turbulence, coherent structures, dynamical systems and symmetry. Zbl 0923.76002
Holmes, Philip; Lumley, John L.; Berkooz, Gal
69
1998
Melnikov’s method and Arnold diffusion for perturbations of integrable Hamiltonian systems. Zbl 0497.70025
Holmes, Philip J.; Marsden, Jerrold E.
68
1982
A magnetoelastic strange attractor. Zbl 0405.73082
Moon, F. C.; Holmes, P. J.
64
1979
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.
63
1993
The dynamics of repeated impacts with a sinusoidally vibrating table. Zbl 0518.73015
Holmes, P. J.
58
1982
Horseshoes and Arnold diffusion for Hamiltonian systems and Lie groups. Zbl 0488.70006
Holmes, Philip J.; Marsden, Jerrold E.
57
1983
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.
53
1982
Knots and links in three-dimensional flows. Zbl 0869.58044
Ghrist, Robert W.; Holmes, Philip J.; Sullivan, Michael C.
51
1997
Cascades of homoclinic orbits to, and chaos near, a Hamiltonian saddle- center. Zbl 0749.58022
Mielke, A.; Holmes, P.; O’Reilly, O.
51
1992
Random perturbations of heteroclinic attractors. Zbl 0702.58038
Stone, Emily; Holmes, Philip
51
1990
Kuramoto-Sivashinsky dynamics on the center-unstable manifold. Zbl 0687.34036
Armbruster, Dieter; Guckenheimer, John; Holmes, Philip
50
1989
Averaging and chaotic motions in forced oscillations. Zbl 0472.70024
Holmes, Philip J.
49
1980
Bifurcations to divergence and flutter in flow-induced oscillations: a finite dimensional analysis. Zbl 0363.73059
Holmes, P. J.
44
1977
Strong NLS soliton-defect interactions. Zbl 1061.35132
Goodman, Roy H.; Holmes, Philip J.; Weinstein, Michael I.
43
2004
The dynamics of legged locomotion: Models, analyses, and challenges. Zbl 1100.34002
Holmes, Philip; Full, Robert J.; Koditschek, Dan; Guckenheimer, John
42
2006
Global existence theory for a generalized Ginzburg-Landau equation. Zbl 0783.35070
Duan, Jinqiao; Holmes, Philip; Titi, Edriss S.
41
1992
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.
41
1980
Bifurcation of periodic motions in two weakly coupled van der Pol oscillators. Zbl 0447.70028
Rand, R. H.; Holmes, P. J.
41
1980
On the dynamics of fine structure. Zbl 0791.35030
Ball, J. M.; Holmes, P. J.; James, R. D.; Pego, R. L.; Swart, P. J.
39
1991
Regularity, approximation and asymptotic dynamics for a generalized Ginzburg-Landau equation. Zbl 0808.35133
Duan, Jinqiao; Titi, Edriss S.; Holmes, Philip
38
1993
Exponentially small splittings of separatrices with applications of KAM theory and degenerate bifurcations. Zbl 0685.70017
Holmes, Philip; Marsden, Jerrold; Scheurle, Jürgen
36
1988
Energy minimization and the formation of microstructure in dynamic anti- plane shear. Zbl 0786.73066
Swart, Pieter J.; Holmes, Philip J.
35
1992
Bifurcation to divergence and flutter in flow-induced oscillations: An infinite dimensional analysis. Zbl 0385.93028
Holmes, Philip; Marsden, Jerrold
33
1978
On the Cauchy problem of a generalized Ginzburg-Landau equation. Zbl 0833.35067
Duan, Jinqiao; Holmes, Philip
32
1994
Bifurcations of one- and two-dimensional maps. Zbl 0556.58023
Holmes, P.; Whitley, D.
30
1984
Nonlinear propagation of light in one-dimensional periodic structures. Zbl 1005.78011
Goodman, R. H.; Weinstein, M. I.; Holmes, P. J.
28
2001
Homoclinic orbits, subharmonics and global bifurcations in forced oscillations. Zbl 0532.58019
Greenspan, B. D.; Holmes, P. J.
27
1983
Knotted periodic orbits in suspensions of Smale’s horseshoe: torus knots and bifurcation sequences. Zbl 0593.58027
Holmes, Philip; Williams, R. F.
26
1985
Second order averaging and bifurcations to subharmonics in Duffing’s equation. Zbl 0478.73028
Holmes, C.; Holmes, P.
26
1981
A periodically forced impact oscillator with large dissipation. Zbl 0539.70032
Shaw, S. W.; Holmes, P. J.
25
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.
24
2002
Spatially complex equilibria of buckled rods. Zbl 0655.73029
Mielke, Alexander; Holmes, Philip
24
1988
Spatial structure of time-periodic solutions of the Ginzburg-Landau equation. Zbl 0618.35003
Holmes, Philip
24
1986
The dynamics of choice among multiple alternatives. Zbl 1139.91028
McMillen, Tyler; Holmes, Philip
23
2006
Periodic orbits in slowly varying oscillators. Zbl 0619.34041
Wiggins, Stephen; Holmes, Philip
23
1987
Repeated resonance and homoclinic bifurcation in a periodically forced family of oscillators. Zbl 0547.34028
Greenspan, Bernie; Holmes, Philip
23
1984
Homoclinic orbits in slowly varying oscillators. Zbl 0622.34041
Wiggins, Stephen; Holmes, Philip
22
1987
Celestial encounters. The origins of chaos and stability. Zbl 0944.37001
Diacu, Florin; Holmes, Philip
21
1996
Low-dimensional modelling of turbulence using the proper orthogonal decomposition: A tutorial. Zbl 1094.76024
Smith, Troy R.; Moehlis, Jeff; Holmes, Philip
20
2005
Constrained Euler buckling: An interplay of computation and analysis. Zbl 0949.74023
Holmes, Philip; Domokos, Gábor; Schmitt, John; Szeberényi, Imre
20
1999
Bifurcations of the forced van der Pol oscillator. Zbl 0375.34031
Holmes, P. J.; Rand, D. A.
20
1978
Chaotic motions in a weakly nonlinear model for surface waves. Zbl 0602.76015
Holmes, Philip
19
1986
Globally coupled oscillator networks. Zbl 1132.92316
Brown, Eric; Holmes, Philip; Moehlis, Jeff
18
2003
Constrained Euler buckling. Zbl 0876.34047
Domokos, G.; Holmes, P.; Royce, B.
18
1997
Fronts, domain walls and pulses in a generalized Ginzburg-Landau equation. Zbl 0820.58053
Duan, Jinqiao; Holmes, Philip
18
1995
Nonlinear stability of axisymmetric swirling flows. Zbl 0658.76044
Szeri, A.; Holmes, P.
18
1988
Mechanical models for insect locomotion: Dynamics and stability in the horizontal plane. I: Theory. Zbl 1033.92005
Schmitt, John; Holmes, Philip
17
2000
Dynamics of the Kirchhoff equations. I: Coincident centers of gravity and buoyancy. Zbl 1194.70009
Holmes, Philip; Jenkins, Jeffrey; Leonard, Naomi Ehrich
17
1998
The existence of transverse homoclinic points in the Sitnikov problem. Zbl 0815.34032
Dankowicz, Harry; Holmes, Philip
17
1995
On a Painlevé-type boundary-value problem. Zbl 0552.34023
Holmes, Philip; Spence, David
17
1984
The bifurcations of Duffing’s equation: An application of catastrophe theory. Zbl 0337.34049
Holmes, P. J.; Rand, D. A.
17
1976
Simple neural networks that optimize decisions. Zbl 1069.92004
Brown, Eric; Gao, Juan; Holmes, Philip; Bogacz, Rafal; Gilzenrat, Mark; Cohen, Jonathan D.
16
2005
On the attracting set for Duffing’s equation. II: A geometrical model for moderate force and damping. Zbl 0574.58024
Holmes, Philip; Whitley, David
16
1983
Minimal models of bursting neurons: How multiple currents, conductances, and timescales affect bifurcation diagrams. Zbl 1090.34039
Ghigliazza, R. M.; Holmes, P.
15
2004
Some remarks on chaotic particle paths in time-periodic, three- dimensional swirling flows. Zbl 0521.76049
Holmes, Philip
15
1984
A simply stabilized running model. Zbl 1088.34517
Ghigliazza, R. M.; Altendorfer, R.; Holmes, P.; Koditschek, D.
14
2003
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
14
1997
Knotted periodic orbits in suspensions of Smale’s horseshoe: period multiplying and cabled knots. Zbl 0623.58014
Holmes, Philip
14
1986
Rapid decision threshold modulation by reward rate in a neural network. Zbl 1103.68726
Simen, Patrick; Cohen, Jonathan D.; Holmes, Philip
13
2006
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
Noise induced intermittency in a model of a turbulent boundary layer. Zbl 0687.76055
Stone, Emily; Holmes, Philip
13
1989
Center manifolds, normal forms and bifurcations of vector fields with application to coupling between periodic and steady motions. Zbl 1194.37075
Holmes, Philip J.
13
1981
A hexapedal jointed-leg model for insect locomotion in the horizontal plane. Zbl 1248.92003
Kukillaya, Raghavendra P.; Holmes, Philip J.
12
2007
Low-dimensional models for turbulent plane Couette flow in a minimal flow unit. Zbl 1108.76031
Smith, T. R.; Moehlis, J.; Holmes, P.
12
2005
Mechanical models for insect locomotion: Dynamics and stability in the horizontal plane. II: Application. Zbl 1039.92006
Schmitt, John; Holmes, Philip
12
2000
Josephson’s junction, annulus maps, Birkhoff attractors, horseshoes and rotation sets. Zbl 0582.58020
Hockett, Kevin; Holmes, Philip
12
1986
The existence of arbitrarily many distinct periodic orbits in a two degree of freedom Hamiltonian system. Zbl 0595.58036
Veerman, Peter; Holmes, Philip
12
1985
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.
11
2010
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 ODE whose solutions contain all knots and links. Zbl 0878.34038
Ghrist, Robert W.; Holmes, Philip J.
11
1996
An elastic rod model for anguilliform swimming. Zbl 1113.92005
McMillan, T.; Holmes, P.
10
2006
A minimal model of a central pattern generator and motoneurons for insect locomotion. Zbl 1090.34040
Ghigliazza, R. M.; Holmes, P.
10
2004
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
Unfolding a degenerate nonlinear oscillator: A codimension two bifurcation. Zbl 0506.34034
Holmes, Philip
10
1980
A simple model for clock-actuated legged locomotion. Zbl 1229.70028
Seipel, J.; Holmes, P.
9
2007
Models for turbulent plane Couette flow using the proper orthogonal decomposition. Zbl 1185.76261
Moehlis, J.; Smith, T. R.; Holmes, P.; Faisst, H.
9
2002
Modeling a simple choice task: Stochastic dynamics of mutually inhibitory neural groups. Zbl 1060.92019
Brown, Eric; Holmes, Philip
9
2001
Homoclinic explosions and implosions. Zbl 0881.58044
Doelman, Arjen; Holmes, Philip
9
1996
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
A strange family of three-dimensional vector fields near a degenerate singularity. Zbl 0421.58016
Holmes, Philip J.
9
1980
Pipes supported at both ends cannot flutter. Zbl 0386.73056
Holmes, P. J.
9
1978
Mechanical models for insect locomotion: Stability and parameter studies. Zbl 1059.70006
Schmitt, John; Holmes, Philip
8
2001
Heteroclinic cycles and modulated travelling waves in a system with \(D_ 4\) symmetry. Zbl 0774.34031
Campbell, Sue Ann; Holmes, Philip
8
1992
The effect of modeled drag reduction on the wall region. Zbl 0708.76072
Aubry, N.; Lumley, J. L.; Holmes, P.
8
1990
Ninety plus thirty years of nonlinear dynamics: less is more and more is different. Zbl 1092.37500
Holmes, Philip
7
2005
Euler buckling in a potential field. Zbl 1139.74415
Holmes, P.; Domokos, G.; Hek, G.
7
2000
Simple models for excitable and oscillatory neural networks. Zbl 0908.92013
Taylor, David; Holmes, Philip
7
1998
Heterogeneous inputs to central pattern generators can shape insect gaits. Zbl 1425.92036
Aminzare, Zahra; Holmes, Philip
1
2019
Gait transitions in a phase oscillator model of an insect central pattern generator. Zbl 1385.92007
Aminzare, Zahra; Srivastava, Vaibhav; Holmes, Philip
5
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
1
2016
Some joys and trials of mathematical neuroscience. Zbl 1293.92006
Holmes, Philip
1
2014
Turbulence, coherent structures, dynamical systems and symmetry. 2nd ed. Zbl 1251.76001
Holmes, Philip; Lumley, John L.; Berkooz, Gahl; Rowley, Clarence W.
97
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
5
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.
11
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
5
2009
A comparison of bounded diffusion models for choice in time controlled tasks. Zbl 1176.60075
Zhang, Jiaxiang; Bogacz, Rafal; Holmes, Philip
4
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.
3
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
6
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.
9
2007
The dynamics of legged locomotion: Models, analyses, and challenges. Zbl 1100.34002
Holmes, Philip; Full, Robert J.; Koditschek, Dan; Guckenheimer, John
42
2006
The dynamics of choice among multiple alternatives. Zbl 1139.91028
McMillen, Tyler; Holmes, Philip
23
2006
Rapid decision threshold modulation by reward rate in a neural network. Zbl 1103.68726
Simen, Patrick; Cohen, Jonathan D.; Holmes, Philip
13
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
20
2005
Simple neural networks that optimize decisions. Zbl 1069.92004
Brown, Eric; Gao, Juan; Holmes, Philip; Bogacz, Rafal; Gilzenrat, Mark; Cohen, Jonathan D.
16
2005
Low-dimensional models for turbulent plane Couette flow in a minimal flow unit. Zbl 1108.76031
Smith, T. R.; Moehlis, J.; Holmes, P.
12
2005
Ninety plus thirty years of nonlinear dynamics: less is more and more is different. Zbl 1092.37500
Holmes, Philip
7
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
A simply stabilized running model. Zbl 1074.70005
Ghigliazza, R. M.; Altendorfer, R.; Holmes, P.; Koditschek, D.
2
2005
On the phase reduction and response dynamics of neural oscillator population. Zbl 1054.92006
Brown, Eric; Moehlis, Jeff; Holmes, Philip
97
2004
Strong NLS soliton-defect interactions. Zbl 1061.35132
Goodman, Roy H.; Holmes, Philip J.; Weinstein, Michael I.
43
2004
Minimal models of bursting neurons: How multiple currents, conductances, and timescales affect bifurcation diagrams. Zbl 1090.34039
Ghigliazza, R. M.; Holmes, P.
15
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
A minimal model of a central pattern generator and motoneurons for insect locomotion. Zbl 1090.34040
Ghigliazza, R. M.; Holmes, P.
10
2004
Globally coupled oscillator networks. Zbl 1132.92316
Brown, Eric; Holmes, Philip; Moehlis, Jeff
18
2003
A simply stabilized running model. Zbl 1088.34517
Ghigliazza, R. M.; Altendorfer, R.; Holmes, P.; Koditschek, D.
14
2003
On nonlinear boundary-value problems: Ghosts, parasites and discretizations. Zbl 1069.34020
Domokos, G.; Holmes, P.
4
2003
Travelling wave solutions of the degenerate Kolmogorov-Petrovski-Piskunov equation. Zbl 1060.35052
Medvedev, G. S.; Ono, K.; Holmes, P. J.
4
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.
1
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.
24
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
Models for turbulent plane Couette flow using the proper orthogonal decomposition. Zbl 1185.76261
Moehlis, J.; Smith, T. R.; Holmes, P.; Faisst, H.
9
2002
On the dynamics of cranes, or spherical pendula with moving supports. Zbl 1346.37069
Ghigliazza, R. M.; Holmes, P.
5
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.
28
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 of turbulence or, the dynamics of coherent structures. Zbl 1007.35059
Holmes, P. J.; Mattingly, J. C.; Wittenberg, R. W.
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
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
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
20
1999
Motions and stability of a piecewise holonomic system: The discrete Chaplygin sleigh. Zbl 1020.70007
Coleman, M. J.; Holmes, P.
5
1999
Constrained Euler buckling: Line contact solutions. Zbl 0983.74024
Holmes, Philip; Schmitt, John; Domokos, Gabor
1
1999
Turbulence, coherent structures, dynamical systems and symmetry. Zbl 0923.76002
Holmes, Philip; Lumley, John L.; Berkooz, Gal
69
1998
Dynamics of the Kirchhoff equations. I: Coincident centers of gravity and buoyancy. Zbl 1194.70009
Holmes, Philip; Jenkins, Jeffrey; Leonard, Naomi Ehrich
17
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
3
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.
51
1997
Constrained Euler buckling. Zbl 0876.34047
Domokos, G.; Holmes, P.; Royce, B.
18
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
14
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
320
1996
Celestial encounters. The origins of chaos and stability. Zbl 0944.37001
Diacu, Florin; Holmes, Philip
21
1996
An ODE whose solutions contain all knots and links. Zbl 0878.34038
Ghrist, Robert W.; Holmes, Philip J.
11
1996
Homoclinic explosions and implosions. Zbl 0881.58044
Doelman, Arjen; Holmes, Philip
9
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
18
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
32
1994
Control of noisy heteroclinic cycles. Zbl 0816.76037
Coller, B. D.; Holmes, Philip; Lumley, John L.
6
1994
Knotting within the gluing bifurcation. Zbl 0864.58045
Holmes, P.; Ghrist, R.
2
1994
Interaction of adjacent bursts in the wall region. Zbl 0830.76040
Coller, B. D.; Holmes, P.; Lumley, J. L.
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
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.
63
1993
Regularity, approximation and asymptotic dynamics for a generalized Ginzburg-Landau equation. Zbl 0808.35133
Duan, Jinqiao; Titi, Edriss S.; Holmes, Philip
38
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
Wavelet analysis of the motion of coherent structures. Zbl 0899.76236
Elezgaray, J.; Berkooz, G.; Holmes, P.
3
1993
Knots and orbit genealogies in three dimensional flows. Zbl 0803.58047
Ghrist, Robert; Holmes, Philip
3
1993
Reduction, stability, instability and bifurcation in rotationally symmetric Hamiltonian systems. Zbl 0782.70015
Zombro, Brett; Holmes, Philip
2
1993
On non-inflectional solutions of non-uniform elasticae. Zbl 0793.73036
Domokos, Gábor; Holmes, Philip
1
1993
Symmetries, heteroclinic cycles and intermittency in fluid flow. Zbl 0788.76008
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.
51
1992
Global existence theory for a generalized Ginzburg-Landau equation. Zbl 0783.35070
Duan, Jinqiao; Holmes, Philip; Titi, Edriss S.
41
1992
Energy minimization and the formation of microstructure in dynamic anti- plane shear. Zbl 0786.73066
Swart, Pieter J.; Holmes, Philip J.
35
1992
Heteroclinic cycles and modulated travelling waves in a system with \(D_ 4\) symmetry. Zbl 0774.34031
Campbell, Sue Ann; Holmes, Philip
8
1992
Nonlinear, nonplanar and nonperiodic vibrations of a string. Zbl 0924.73127
O’Reilly, O.; Holmes, P. J.
6
1992
...and 82 more Documents
all top 5

Cited by 7,877 Authors

77 Holmes, Philip J.
55 Li, Jibin
48 Llibre, Jaume
43 Luo, Zhendong
37 Yu, Pei
34 Jing, Zhujun
33 Zhang, Weinian
29 Ashwin, Peter
27 Marsden, Jerrold Eldon
26 Chen, Guanrong
26 Knobloch, Edgar
25 Xu, Wei
24 Moehlis, Jeff
24 Rodríguez-Luis, Alejandro J.
23 Algaba, Antonio
23 Yagasaki, Kazuyuki
21 Haller, George
21 Rand, Richard H.
20 Fečkan, Michal
20 Han, Maoan
20 Luo, Albert C. J.
20 Volkwein, Stefan
20 Zhang, Wei
19 Champneys, Alan R.
19 Feichtinger, Gustav
19 Jiang, Weihua
18 Balasuriya, Sanjeeva
18 Kevrekidis, Ioannis George
18 Yang, Qigui
17 Guo, Boling
17 Lu, Qishao
17 Noack, Bernd R.
17 Stewart, Ian Nicholas
16 Golubitsky, Martin A.
16 Guckenheimer, John M.
16 Iliescu, Traian
16 M-Seara, Tere
16 Shen, Jianwei
16 Wiggins, Stephen
15 Aubry, Nadine
15 Buonomo, Bruno
15 Kühn, Christian
15 Kutz, J. Nathan
14 Broer, Henk W.
14 Brunton, Steven L.
14 Gardini, Laura
14 Krauskopf, Bernd
14 Kuznetsov, Yuri Alexandrovich
14 Rega, Giuseppe
14 Xie, Jianhua
14 Yorke, James Alan
13 Doelman, Arjen
13 Duan, Jinqiao
13 Guo, Shangjiang
13 Lacitignola, Deborah
13 Leung, Andrew Yee-Tak
13 Liu, Qian
13 Liu, Zhengrong
13 Lumley, John Leask
13 Wiercigroch, Marian
13 Wilson, Dan D.
12 Akhmet, Marat Ubaydulla
12 Awrejcewicz, Jan
12 Campbell, Sue Ann
12 Cao, Hongjun
12 Freire Macías, Emilio
12 Grebogi, Celso
12 Huseyin, Koncay
12 Kooi, Bob W.
12 Merino, Manuel
12 Navon, Ionel Michael
12 Piqueira, José Roberto Castilho
12 Rom-Kedar, Vered
12 Rowley, Clarence W.
12 Sapsis, Themistoklis P.
12 Xu, Jian
11 Battelli, Flaviano
11 Bi, Qinsheng
11 Bishop, Steven R.
11 Cao, Qingjie
11 Chen, Yushu
11 Gamero, Estanislao
11 Gao, Hongjun
11 Labouriau, Isabel S.
11 Lenci, Stefano
11 Mezić, Igor
11 Osinga, Hinke Maria
11 Proctor, Joshua L.
11 Rinaldi, Sergio
11 Teixeira, Marco Antonio
11 Vakakis, Alexander F.
11 Wirl, Franz
11 Zgliczyński, Piotr
10 Aihara, Kazuyuki
10 Blackmore, Denis L.
10 Bountis, Tassos C.
10 Chossat, Pascal
10 Govaerts, Willy J. F.
10 Jiang, Guirong
10 Kaper, Tasso J.
...and 7,777 more Authors
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Cited in 462 Serials

605 Physica D
389 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
328 Chaos, Solitons and Fractals
230 Nonlinear Dynamics
160 Journal of Differential Equations
155 Chaos
144 Journal of Fluid Mechanics
143 Applied Mathematics and Computation
119 Communications in Nonlinear Science and Numerical Simulation
92 Journal of Mathematical Analysis and Applications
88 Journal of Computational Physics
85 Physics Letters. A
85 Physics of Fluids
84 Journal of Nonlinear Science
61 SIAM Journal on Applied Dynamical Systems
60 Journal of Mathematical Biology
59 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
59 Applied Mathematics and Mechanics. (English Edition)
56 Journal of Computational and Applied Mathematics
54 Journal of Dynamics and Differential Equations
54 Nonlinear Analysis. Real World Applications
51 Computer Methods in Applied Mechanics and Engineering
49 Dynamics and Stability of Systems
48 Journal of Statistical Physics
44 Automatica
43 Mathematical and Computer Modelling
42 Biological Cybernetics
42 Communications in Mathematical Physics
40 Applied Mathematical Modelling
40 Nonlinear Analysis. Theory, Methods & Applications
39 Mathematical Biosciences
39 Journal of Economic Dynamics & Control
38 ZAMP. Zeitschrift für angewandte Mathematik und Physik
38 Journal of Theoretical Biology
37 Computers and Fluids
36 Journal of Mathematical Physics
35 Neural Computation
34 Computers & Mathematics with Applications
34 Mathematical Problems in Engineering
32 Bulletin of Mathematical Biology
31 Discrete and Continuous Dynamical Systems. Series B
31 Advances in Difference Equations
30 Regular and Chaotic Dynamics
29 Acta Mechanica
28 Systems & Control Letters
27 Archive for Rational Mechanics and Analysis
27 Journal of Computational Neuroscience
27 Discrete Dynamics in Nature and Society
25 Physica A
25 Acta Mathematicae Applicatae Sinica. English Series
25 Dynamical Systems
24 Transactions of the American Mathematical Society
23 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics
22 Mathematics and Computers in Simulation
22 Meccanica
20 International Journal of Engineering Science
20 Mathematical Methods in the Applied Sciences
20 Theoretical and Computational Fluid Dynamics
20 Applied Mathematics Letters
19 Journal of Vibration and Control
18 Journal of the Franklin Institute
18 Nonlinearity
18 Studies in Applied Mathematics
18 Theoretical Population Biology
18 Acta Applicandae Mathematicae
17 International Journal for Numerical Methods in Fluids
17 Journal of Mathematical Psychology
17 Applied Numerical Mathematics
17 Abstract and Applied Analysis
16 International Journal for Numerical Methods in Engineering
16 European Journal of Mechanics. A. Solids
15 International Journal of Control
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15 Topology and its Applications
15 Ergodic Theory and Dynamical Systems
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13 Journal of the Mechanics and Physics of Solids
13 Physics Reports
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13 Celestial Mechanics and Dynamical Astronomy
12 International Journal of Theoretical Physics
12 Reports on Mathematical Physics
12 Journal of Economic Theory
12 Journal of Optimization Theory and Applications
12 The Journal of Mathematical Neuroscience
11 International Journal of Modern Physics B
11 Journal of Economics
11 International Journal of Robust and Nonlinear Control
11 SIAM Journal on Scientific Computing
11 Journal of Biological Dynamics
10 Wave Motion
10 Proceedings of the American Mathematical Society
10 Numerical Methods for Partial Differential Equations
10 Advances in Computational Mathematics
10 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences
10 Acta Mechanica Sinica
10 Journal of Applied Analysis and Computation
9 Applicable Analysis
...and 362 more Serials
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Cited in 58 Fields

2,490 Dynamical systems and ergodic theory (37-XX)
2,002 Ordinary differential equations (34-XX)
898 Biology and other natural sciences (92-XX)
871 Fluid mechanics (76-XX)
829 Partial differential equations (35-XX)
801 Mechanics of particles and systems (70-XX)
548 Numerical analysis (65-XX)
436 Systems theory; control (93-XX)
390 Mechanics of deformable solids (74-XX)
242 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
136 Probability theory and stochastic processes (60-XX)
122 Computer science (68-XX)
121 Statistical mechanics, structure of matter (82-XX)
107 Calculus of variations and optimal control; optimization (49-XX)
100 Difference and functional equations (39-XX)
84 Information and communication theory, circuits (94-XX)
74 Optics, electromagnetic theory (78-XX)
74 Classical thermodynamics, heat transfer (80-XX)
74 Quantum theory (81-XX)
69 Global analysis, analysis on manifolds (58-XX)
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23 Relativity and gravitational theory (83-XX)
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17 History and biography (01-XX)
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5 Sequences, series, summability (40-XX)
5 Algebraic topology (55-XX)
3 Field theory and polynomials (12-XX)
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3 Mathematics education (97-XX)
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