Philip Holmes - Google Scholar Citations · Chaos and fractals: The mathematics behind the computer graphics RL Devaney American Mathematical Soc. 118 1989 Cascades of homoclinic

$Page 1: Philip Holmes - Google Scholar Citations · Chaos and fractals: The mathematics behind the computer graphics RL Devaney American Mathematical Soc. 118 1989 Cascades of homoclinic$
Philip HolmesProfessor of Applied & ComputationalMathematics, Princeton UniversityApplied Mathematics, Solid, Fluid andClassical Mechanics, Biomechanics,Neuroscience

Google ScholarCitation indices All Since 2009Citations 36634 11489h-index 68 40i10-index 220 123

Title Cited by Year

Nonlinear oscillations, dynamical systems, and bifurcations ofvector fieldsJ Guckenheimer, P HolmesNew York

15739 1983

Turbulence, coherent structures, dynamical systems andsymmetryP Holmes, JL Lumley, G BerkoozCambridge university press

2488 1998

The proper orthogonal decomposition in the analysis of turbulentflowsG Berkooz, P Holmes, JL LumleyAnnual review of fluid mechanics 25 (1), 539-575

1565 1993

The dynamics of coherent structures in the wall region of aturbulent boundary layerN Aubry, P Holmes, JL Lumley, E StoneJournal of Fluid Mechanics 192, 115-173

988 1988

A periodically forced piecewise linear oscillatorSW Shaw, PJ HolmesJournal of Sound and Vibration 90 (1), 129-155

732 1983

A nonlinear oscillator with a strange attractorP HolmesPhilosophical Transactions of the Royal Society of London. Series A ...

687 1979

The physics of optimal decision making: a formal analysis ofmodels of performance in two-alternative forced-choice tasks.R Bogacz, E Brown, J Moehlis, P Holmes, JD CohenPsychological review 113 (4), 700

560 2006

The nature of the coupling between segmental oscillators of thelamprey spinal generator for locomotion: a mathematical modelAH Cohen, PJ Holmes, RH RandJournal of mathematical biology 13 (3), 345-369

463 1982

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Philip Holmes - Google Scholar Citations http://scholar.google.com/citations?hl=en&user=HkPSfzgAA...

1 of 21 9/20/14 3:07 PM

Title Cited by Year

A magnetoelastic strange attractorFC Moon, PJ HolmesJournal of Sound and Vibration 65 (2), 275-296

437 1979

The dynamics of repeated impacts with a sinusoidally vibratingtablePJ HolmesJournal of Sound and Vibration 84 (2), 173-189

381 1982

The dynamics of legged locomotion: Models, analyses, andchallengesP Holmes, RJ Full, D Koditschek, J GuckenheimerSiam Review 48 (2), 207-304

295 2006

Heteroclinic cycles and modulated travelling waves in systemswith O (2) symmetryD Armbruster, J Guckenheimer, P HolmesPhysica D: Nonlinear Phenomena 29 (3), 257-282

295 1988

On the phase reduction and response dynamics of neuraloscillator populationsE Brown, J Moehlis, P HolmesNeural computation 16 (4), 673-715

277 2004

A partial differential equation with infinitely many periodic orbits:chaotic oscillations of a forced beamP Holmes, J MarsdenArchive for Rational Mechanics and Analysis 76 (2), 135-165

271 1981

Melnikov’s method and Arnold diffusion for perturbations ofintegrable Hamiltonian systemsPJ Holmes, JE MarsdenJournal of Mathematical Physics 23 (4), 669-675

233 1982

Horseshoes and Arnold diffusion for Hamiltonian systems on LiegroupsPJ Holmes, JE MarsdenCALIFORNIA UNIV BERKELEY CENTER FOR PURE AND APPLIEDMATHEMATICS

229 1981

Celestial encounters: the origins of chaos and stabilityF Diacu, P HolmesPrinceton University Press

221 1996

Horseshoes in perturbations of Hamiltonian systems with two219 1982


2 of 21 9/20/14 3:07 PM

Title Cited by Year

degrees of freedomPJ Holmes, JE MarsdenCommunications in Mathematical Physics 82 (4), 523-544

Structurally stable heteroclinic cyclesJ Guckenheimer, P HolmesMathematical Proceedings of the Cambridge Philosophical Society 103 (01 ...

218 1988

Bifurcation of periodic motions in two weakly coupled van der PoloscillatorsRH Rand, PJ HolmesInternational Journal of Non-Linear Mechanics 15 (4), 387-399

208 1980

Bifurcations to divergence and flutter in flow-induced oscillations: afinite dimensional analysisPJ HolmesJournal of Sound and Vibration 53 (4), 471-503

207 1977

Mechanical models for insect locomotion: dynamics and stability inthe horizontal plane I. TheoryJ Schmitt, P HolmesBiological cybernetics 83 (6), 501-515

172 2000

Strange attractors and chaos in nonlinear mechanicsPJ Holmes, FC MoonJournal of Applied Mechanics 50 (4b), 1021-1032

172 1983

Averaging and chaotic motions in forced oscillationsPJ HolmesSIAM Journal on Applied Mathematics 38 (1), 65-80

167 1980

Exponentially small splittings of separatrices with applications toKAM theory and degenerate bifurcationsP Holmes, J Marsden, J ScheurleAmerican Mathematical Society

163 1988

Systems of coupled oscillators as models of central patterngeneratorsRH Rand, AH Cohen, PJ HolmesNeural control of rhythmic movements in vertebrates, 333-367

158 1988

Kuramoto-Sivashinsky dynamics on the center-unstable manifoldD Armbruster, J Guckenheimer, P HolmesSIAM Journal on Applied Mathematics 49 (3), 676-691

157 1989


3 of 21 9/20/14 3:07 PM

Title Cited by Year

Knots and links in three-dimensional flowsRW Ghrist, PJ Holmes, MC SullivanBooks, Monographs and Lecture Notes, 1

146 1997

Low-dimensional models of coherent structures in turbulencePJ Holmes, JL Lumley, G Berkooz, JC Mattingly, RW WittenbergPhysics Reports 287 (4), 337-384

144 1997

Periodically forced linear oscillator with impacts: chaos andlong-period motionsSW Shaw, P HolmesPhysical Review Letters 51 (8), 623

143 1983

Quantifying dynamic stability and maneuverability in leggedlocomotionRJ Full, T Kubow, J Schmitt, P Holmes, D KoditschekIntegrative and comparative biology 42 (1), 149-157

141 2002

Bifurcation to divergence and flutter in flow-induced oscillations: aninfinite dimensional analysisP Holmes, J MarsdenAutomatica 14 (4), 367-384

139 1978

A periodically forced impact oscillator with large dissipationSW Shaw, PJ HolmesJournal of Applied Mechanics 50 (4a), 849-857

131 1983

Phase portraits and bifurcations of the non-linear oscillator: ẍ+(α+γx2+ βx+ δx3= 0P Holmes, D RandInternational Journal of Non-Linear Mechanics 15 (6), 449-458

129 1980

On the dynamics of fine structureJM Ball, PJ Holmes, RD James, RL Pego, PJ SwartJournal of Nonlinear Science 1 (1), 17-70

125 1991

Random perturbations of heteroclinic attractorsE Stone, P HolmesSIAM Journal on Applied Mathematics 50 (3), 726-743

125 1990

The bifurcations of Duffing's equation: An application ofcatastrophe theoryPJ Holmes, DA RandJournal of Sound and Vibration 44 (2), 237-253

124 1976


4 of 21 9/20/14 3:07 PM

Title Cited by Year

Hamiltonian dynamics of dispersion-managed breathersJN Kutz, P Holmes, SG Evangelides, JP GordonJOSA B 15 (1), 87-96

123 1998

A simply stabilized running modelRM Ghigliazza, R Altendorfer, P Holmes, D KoditschekSIAM Journal on Applied Dynamical Systems 2 (2), 187-218

121 2003

Chaos and fractals: The mathematics behind the computergraphicsRL DevaneyAmerican Mathematical Soc.

118 1989

Cascades of homoclinic orbits to, and chaos near, a Hamiltoniansaddle-centerA Mielke, P Holmes, O O'ReillyJournal of Dynamics and Differential Equations 4 (1), 95-126

117 1992

Knotted periodic orbits in suspensions of Smale's horseshoe: torusknots and bifurcation sequencesP Holmes, RF WilliamsArchive for Rational Mechanics and Analysis 90 (2), 115-194

114 1985

Poincaré, celestial mechanics, dynamical-systems theory and“chaos”P HolmesPhysics Reports 193 (3), 137-163

113 1990

Pipes supported at both ends cannot flutterPJ HolmesJournal of Applied Mechanics 45 (3), 619-622

113 1978

Low-dimensional modelling of turbulence using the properorthogonal decomposition: a tutorialTR Smith, J Moehlis, P HolmesNonlinear Dynamics 41 (1-3), 275-307

111 2005

Spatially complex equilibria of buckled rodsA Mielke, P HolmesArchive for rational Mechanics and Analysis 101 (4), 319-348

110 1988

Bifurcations of one-and two-dimensional mapsP Holmes, D WhitleyPhilosophical Transactions of the Royal Society of London. Series A ...

109 1984


5 of 21 9/20/14 3:07 PM

Title Cited by Year

Second order averaging and bifurcations to subharmonics inDuffing's equationC Holmes, P HolmesJournal of Sound and Vibration 78 (2), 161-174

108 1981

Homoclinic orbits, subharmonics and global bifurcations in forcedoscillationsBD Greenspan, PJ HolmesCALIFORNIA UNIV BERKELEY CENTER FOR PURE AND APPLIEDMATHEMATICS

106 1981

Dynamics and stability of legged locomotion in the horizontalplane: a test case using insectsJ Schmitt, M Garcia, RC Razo, P Holmes, RJ FullBiological cybernetics 86 (5), 343-353

103 2002

Mechanical models for insect locomotion: dynamics and stability inthe horizontal plane–II. ApplicationJ Schmitt, P HolmesBiological cybernetics 83 (6), 517-527

100 2000

Bifurcations of the forced van der Pol oscillatorPJ Holmes, DA RandQuarterly of Applied Mathematics 35, 495-509

96 1978

Regularity, approximation and asymptotic dynamics for ageneralized Ginzburg-Landau equationJ Duan, ES Titi, P HolmesNonlinearity 6 (6), 915

95 1993

Simple neural networks that optimize decisionsE Brown, J Gao, P Holmes, R Bogacz, M Gilzenrat, JD CohenInternational Journal of Bifurcation and Chaos 15 (03), 803-826

93 2005

Turbulence, coherent structures, dynamical systems andsymmetryP HolmesCambridge University Press

91 2012

Center manifolds, normal forms and bifurcations of vector fieldswith application to coupling between periodic and steady motionsPJ HolmesPhysica D: Nonlinear Phenomena 2 (3), 449-481

91 1981

Rapid decision threshold modulation by reward rate in a neural90 2006


6 of 21 9/20/14 3:07 PM

Title Cited by Year

networkP Simen, JD Cohen, P HolmesNeural networks 19 (8), 1013-1026

The dynamics of choice among multiple alternativesT McMillen, P HolmesJournal of Mathematical Psychology 50 (1), 30-57

89 2006

Repeated resonance and homoclinic bifurcation in a periodicallyforced family of oscillatorsB Greenspan, P HolmesSIAM journal on mathematical analysis 15 (1), 69-97

86 1984

Homoclinic orbits in slowly varying oscillatorsS Wiggins, P HolmesSIAM journal on mathematical analysis 18 (3), 612-629

82 1987

Origin of oscillations in visual cortex: feedback versus localcouplingDM Kammen, PJ Holmes, C KochModels of Brain Functions, 273-284

81 1989

Constrained euler bucklingG Domokos, P Holmes, B RoyceJournal of Nonlinear Science 7 (3), 281-314

74 1997

Energy minimization and the formation of microstructure indynamic anti-plane shearPJ Swart, PJ HolmesArchive for rational mechanics and analysis 121 (1), 37-85

74 1992

Stability analysis of legged locomotion models by symmetry-factored return mapsR Altendorfer, DE Koditschek, P HolmesThe International Journal of Robotics Research 23 (10-11), 979-999

71 2004

Chaotic motions in a weakly nonlinear model for surface wavesP HolmesJournal of Fluid Mechanics 162, 365-388

71 1986

Dynamics and stability of insect locomotion: a hexapedal model forhorizontal plane motionsJE Seipel, PJ Holmes, RJ FullBiological cybernetics 91 (2), 76-90

68 2004


7 of 21 9/20/14 3:07 PM

Title Cited by Year

Globally coupled oscillator networksE Brown, P Holmes, J MoehlisPerspectives and Problems in Nolinear Science, 183-215

68 2003

On the attracting set for Duffing's equation: II. A geometrical modelfor moderate force and dampingP Holmes, D WhitleyPhysica D: Nonlinear Phenomena 7 (1), 111-123

68 1983

Reward rate optimization in two-alternative decision making:empirical tests of theoretical predictions.P Simen, D Contreras, C Buck, P Hu, P Holmes, JD CohenJournal of Experimental Psychology: Human Perception and Performance 35 (6...

66 2009

A model of interval timing by neural integrationP Simen, F Balci, JD Cohen, P HolmesThe Journal of Neuroscience 31 (25), 9238-9253

64 2011

Mechanisms underlying dependencies of performance on stimulushistory in a two-alternative forced-choice taskRY Cho, LE Nystrom, ET Brown, AD Jones, TS Braver, PJ Holmes, ...Cognitive, Affective, & Behavioral Neuroscience 2 (4), 283-299

63 2002

A simply stabilized running modelRM Ghigliazza, R Altendorfer, P Holmes, D KoditschekSIAM review 47 (3), 519-549

62 2005

Nonlinear propagation of light in one-dimensional periodicstructuresRH Goodman, MI Weinstein, PJ HolmesJournal of Nonlinear Science 11 (2), 123-168

62 2001

Non-linear, non-planar and non-periodic vibrations of a stringO O'Reilly, PJ HolmesJournal of Sound and Vibration 153 (3), 413-435

62 1992

Running in three dimensions: Analysis of a point-mass sprung-legmodelJE Seipel, P HolmesThe International Journal of Robotics Research 24 (8), 657-674

60 2005

UNFOLDING A DEGENERATE NONLINEAR OSCILLATOR: ACODIMENSION TWO BIFURCATION*P HolmesAnnals of the New York Academy of Sciences 357 (1), 473-488

60 1980


8 of 21 9/20/14 3:07 PM

Title Cited by Year

Knotted periodic orbits in suspensions of Smale's horseshoe:period multiplying and cabled knotsP HolmesPhysica D: Nonlinear Phenomena 21 (1), 7-41

59 1986

Spatial structure of time-periodic solutions of the Ginzburg-LandauequationP HolmesPhysica D: Nonlinear Phenomena 23 (1), 84-90

57 1986

A simple model for clock-actuated legged locomotionJ Seipel, P HolmesRegular and chaotic dynamics 12 (5), 502-520

55 2007

Josephson's junction, annulus maps, Birkhoff attractors,horseshoes and rotation setsK Hockett, P HolmesErgodic theory and dynamical systems 6 (02), 205-239

53 1986

Constrained Euler buckling: an interplay of computation andanalysisP Holmes, G Domokos, J Schmitt, I SzeberényiComputer Methods in Applied Mechanics and Engineering 170 (3), 175-207

52 1999

Mode-locking pulse dynamics in a fiber laser with a saturableBragg reflectorJN Kutz, BC Collings, K Bergman, S Tsuda, ST Cundiff, WH Knox, ...JOSA B 14 (10), 2681-2690

52 1997

The influence of spike rate and stimulus duration on noradrenergicneuronsE Brown, J Moehlis, P Holmes, E Clayton, J Rajkowski, G Aston-JonesJournal of Computational Neuroscience 17 (1), 13-29

51 2004

Intermittent dynamics in simple models of the turbulent wall layerG Berkooz, P Holmes, JL LumleyJournal of Fluid Mechanics 230, 75-95

51 1991

Noise induced intermittency in a model of a turbulent boundarylayerE Stone, P HolmesPhysica D: Nonlinear Phenomena 37 (1), 20-32

48 1989

Stability analysis of a clock-driven rigid-body SLIP model for RHexR Altendorfer, DE Koditschek, P HolmesThe International Journal of Robotics Research 23 (10-11), 1001-1012

47 2004


9 of 21 9/20/14 3:07 PM

Title Cited by Year

A minimal model of a central pattern generator and motoneuronsfor insect locomotionRM Ghigliazza, P HolmesSIAM Journal on Applied Dynamical Systems 3 (4), 671-700

46 2004

Dynamics of the Kirchhoff equations I: Coincident centers ofgravity and buoyancyP Holmes, J Jenkins, NE LeonardPhysica D: Nonlinear Phenomena 118 (3), 311-342

46 1998

Euler's problem, Euler's method, and the standard map; or, thediscrete charm of bucklingG Domokos, P HolmesJournal of Nonlinear Science 3 (1), 109-151

46 1993

Evidence for homoclinic orbits as a precursor to chaos in amagnetic pendulumFC Moon, J Cusumano, PJ HolmesPhysica D: Nonlinear Phenomena 24 (1), 383-390

46 1987

Modeling a simple choice task: stochastic dynamics of mutuallyinhibitory neural groupsE Brown, P HolmesStochastics and dynamics 1 (02), 159-191

45 2001

Nonlinear stability of axisymmetric swirling flowsA Szeri, P HolmesPhilosophical Transactions of the Royal Society of London. Series A ...

45 1988

Do humans produce the speed–accuracy trade-off that maximizesreward rate?R Bogacz, PT Hu, PJ Holmes, JD CohenThe Quarterly Journal of Experimental Psychology 63 (5), 863-891

44 2010

On the Cauchy problem of a generalized Ginzburg–LandauequationJ Duan, P HolmesNonlinear Analysis: Theory, Methods & Applications 22 (8), 1033-1040

44 1994

lN NONLINEAR OSCILLATORSP HolmesNew directions in dynamical systems 127, 150

44 1988

Periodic orbits in slowly varying oscillatorsS Wiggins, P HolmesSIAM journal on mathematical analysis 18 (3), 592-611

44 1987


10 of 21 9/20/14 3:07 PM

Title Cited by Year

Models for turbulent plane Couette flow using the properorthogonal decompositionJ Moehlis, TR Smith, P Holmes, H FaisstPhysics of Fluids (1994-present) 14 (7), 2493-2507

43 2002

Can monkeys choose optimally when faced with noisy stimuli andunequal rewards?S Feng, P Holmes, A Rorie, WT NewsomePLoS computational biology 5 (2), e1000284

42 2009

Some remarks on chaotic particle paths in time-periodic, three-dimensional swirling flowsPJ HolmesContemp. Math 28, 393-404

42 1984

Minimal models of bursting neurons: How multiple currents,conductances, and timescales affect bifurcation diagramsRM Ghigliazza, P HolmesSIAM Journal on Applied Dynamical Systems 3 (4), 636-670

41 2004

The limited effectiveness of normal forms: A critical review andextension of local bifurcation studies of the Brusselator PDERW Wittenberg, P HolmesPhysica D: Nonlinear Phenomena 100 (1), 1-40

40 1997

Exponentially small estimates for separatrix splittingsJ Scheurle, JE Marsden, P HolmesAsymptotics beyond All Orders, 187-195

39 1991

‘Strange’phenomena in dynamical systems and their physicalimplicationsP HolmesApplied Mathematical Modelling 1 (7), 362-366

39 1977

Oscillatory thermomechanical instability of an ultrathin catalystF Cirak, JE Cisternas, AM Cuitino, G Ertl, P Holmes, IG Kevrekidis, M Ortiz, ...Science 300 (5627), 1932-1936

38 2003

Scale and space localization in the Kuramoto–SivashinskyequationRW Wittenberg, P HolmesChaos: An Interdisciplinary Journal of Nonlinear Science 9 (2), 452-465

38 1999

A strange family of three-dimensional vector fields near adegenerate singularity 38 1980


11 of 21 9/20/14 3:07 PM

Title Cited by Year

PJ HolmesJournal of Differential Equations 37 (3), 382-403

Acquisition of decision making criteria: reward rate ultimately beatsaccuracyF Balci, P Simen, R Niyogi, A Saxe, JA Hughes, P Holmes, JD CohenAttention, Perception, & Psychophysics 73 (2), 640-657

37 2011

Mechanical models for insect locomotion: stability and parameterstudiesJ Schmitt, P HolmesPhysica D: Nonlinear Phenomena 156 (1), 139-168

37 2001

Dynamics of a nonlinear oscillator with feedback control I: localanalysisP HolmesJournal of dynamic systems, measurement, and control 107 (2), 159-165

37 1985

Bifurcation sequences in horseshoe maps: infinitely many routesto chaosP HolmesPhysics Letters A 104 (6), 299-302

37 1984

Low-dimensional models for turbulent plane Couette flow in aminimal flow unitTR Smith, J Moehlis, P HolmesJournal of Fluid Mechanics 538, 71-110

36 2005

Interaction of sine-Gordon kinks with defects: Phase spacetransport in a two-mode modelRH Goodman, PJ Holmes, MI WeinsteinPhysica D: Nonlinear Phenomena 161 (1), 21-44

36 2002

Power spectra of strange attractors near homoclinic orbitsV Brunsden, P HolmesPhysical review letters 58 (17), 1699

36 1987

Can dynamical systems approach turbulence?P HolmesWhither Turbulence? Turbulence at the crossroads, 195-249

35 1990

On linearly coupled relaxation oscillationsJ Bélair, P HolmesQuarterly of applied mathematics 42 (2), 193-219

34 1984


12 of 21 9/20/14 3:07 PM

Title Cited by Year

An elastic rod model for anguilliform swimmingT McMillen, P HolmesJournal of mathematical biology 53 (5), 843-886

33 2006

The existence of transverse homoclinic points in the SitnikovproblemH Dankowicz, P HolmesJournal of differential equations 116 (2), 468-483

33 1995

Control of bursting in boundary layer modelsBD Coller, P Holmes, JL LumleyApplied Mechanics Reviews 47 (6S), S139-S143

33 1994

Proof of non-integrability for the Henon-Heiles Hamiltonian near anexceptional integrable caseP HolmesPhysica D: Nonlinear Phenomena 5 (2), 335-347

33 1982

A hexapedal jointed-leg model for insect locomotion in thehorizontal planeRP Kukillaya, PJ HolmesBiological cybernetics 97 (5-6), 379-395

32 2007

Fronts, domain walls and pulses in a generalized Ginzburg-Landau equationJ Duan, P HolmesProceedings of the Edinburgh Mathematical Society (Series 2) 38 (01), 77-97

31 1995

On a Painlevé-type boundary-value problemP Holmes, D SpenceThe Quarterly Journal of Mechanics and Applied Mathematics 37 (4), 525-538

31 1984

New approaches to nonlinear problems in dynamicsPJ HolmesSiam

31 1980

Optimal decisions: From neural spikes, through stochasticdifferential equations, to behaviorP Holmes, SB Eric, J Moehlis, R Bogacz, GAO Juan, G Aston-Jones, ...IEICE Transactions on Fundamentals of Electronics, Communications and ...

30 2005

On the dynamics of cranes, or spherical pendula with movingsupportsRM Ghigliazza, P HolmesInternational Journal of Non-Linear Mechanics 37 (7), 1211-1221

30 2002


13 of 21 9/20/14 3:07 PM

Title Cited by Year

Optimality and robustness of a biophysical decision-making modelunder norepinephrine modulationP Eckhoff, KF Wong-Lin, P HolmesThe Journal of Neuroscience 29 (13), 4301-4311

29 2009

Turbulence, coherent structures, dynamical systems andsymmetryG Berkooz, P Holmes, JL LumleyCambridge Monographs on Mechanics, Cambridge University Press

29 1996

Power spectra of chaotic vibrations of a buckled beamV Brunsden, J Cortell, PJ HolmesJournal of sound and vibration 130 (1), 1-25

29 1989

Addendum: A magnetoelastic strange attractor:(1979 Journal ofSound and Vibration65, 275–296)PJ Holmes, FC MoonJournal of Sound and Vibration 69 (2), 339

29 1980

Dynamical systems and models for reversals of the earth'smagnetic fieldDRJ Chillingworth, PJ HolmesJournal of the International Association for Mathematical Geology 12 (1), 41-59

29 1980

On diffusion processes with variable drift rates as models fordecision making during learningP Eckhoff, P Holmes, C Law, PM Connolly, JI GoldNew journal of physics 10 (1), 015006

28 2008

CO oxidation on thin Pt crystals: Temperature slaving and thederivation of lumped modelsJ Cisternas, P Holmes, IG Kevrekidis, X LiThe Journal of chemical physics 118 (7), 3312-3328

28 2003

An ODE whose solutions contain all knots and linksRW Ghrist, PJ HolmesInternational Journal of Bifurcation and Chaos 6 (05), 779-800

28 1996

Observations regarding ‘‘Coherence and chaos in a model ofturbulent boundary layer’’by X. Zhou and L. Sirovich [Phys. FluidsA 4, 2855 (1992)]G Berkooz, P Holmes, JL Lumley, N Aubry, E StonePhysics of Fluids (1994-present) 6 (4), 1574-1578

28 1994


14 of 21 9/20/14 3:07 PM

Title Cited by Year

Unstable fixed points, heteroclinic cycles and exponential tails inturbulence productionE Stone, P HolmesPhysics Letters A 155 (1), 29-42

28 1991

Bifurcation and chaos in a simple feedback control systemP HolmesDecision and Control, 1983. The 22nd IEEE Conference on 22, 365-370

28 1983

Sequential effects in two-choice reaction time tasks:decomposition and synthesis of mechanismsJ Gao, KF Wong-Lin, P Holmes, P Simen, JD CohenNeural computation 21 (9), 2407-2436

27 2009

Simple models for excitable and oscillatory neural networksD Taylor, P HolmesJournal of mathematical biology 37 (5), 419-446

27 1998

Turbulence, coherent structures, symmetry and dynamicalsystemsP Holmes, JL Lumley, G BerkoozCambridge Monographs on Mechanics and Applied Mathematics. Cambridge ...

27 1996

Lumley, and G. BerkoozJL HolmesTurbulence, Coherence Structure, Dynamical Systems and Symmetry

27 1996

Mechanical models for insect locomotion: active muscles andenergy lossesJ Schmitt, P HolmesBiological cybernetics 89 (1), 43-55

26 2003

Control of noisy heteroclinic cyclesBD Coller, P Holmes, JL LumleyPhysica D: Nonlinear Phenomena 72 (1), 135-160

26 1994

On the relation between low-dimensional models and thedynamics of coherent structures in the turbulent wall layerG Berkooz, P Holmes, JL LumleyTheoretical and Computational Fluid Dynamics 4 (6), 255-269

26 1993

Knotted periodic orbits in suspensions of annulus mapsPJ HolmesProceedings of the Royal Society of London. A. Mathematical and Physical ...

26 1987


15 of 21 9/20/14 3:07 PM

Title Cited by Year

Nonlinear muscles, passive viscoelasticity and body taperconspire to create neuromechanical phase lags in anguilliformswimmersT McMillen, T Williams, P HolmesPLoS computational biology 4 (8), e1000157

25 2008

A neural network model of the Eriksen task: Reduction, analysis,and data fittingYS Liu, P Holmes, JD CohenNeural Computation 20 (2), 345-373

25 2008

Neuromechanical models for insect locomotion: Stability,maneuverability, and proprioceptive feedbackR Kukillaya, J Proctor, P HolmesCHAOS: An Interdisciplinary Journal of Nonlinear Science 19 (2), 026107

24 2009

Ninety plus thirty years of nonlinear dynamics: Less is more andmore is differentP HolmesInternational Journal of Bifurcation and Chaos 15 (09), 2703-2716

24 2005

Knotted periodic orbits in suspensions of Smale's horseshoe:extended families and bifurcation sequencesP HolmesPhysica D: Nonlinear Phenomena 40 (1), 42-64

24 1989

The existence of arbitrarily many distinct periodic orbits in a twodegree of freedom Hamiltonian systemP Veerman, P HolmesPhysica D: Nonlinear Phenomena 14 (2), 177-192

24 1985

How well can spring-mass-like telescoping leg models fitmulti-pedal sagittal-plane locomotion data?M Srinivasan, P HolmesJournal of theoretical biology 255 (1), 1-7

23 2008

Three-dimensional translational dynamics and stability of multi-legged runnersJ Seipel, P HolmesThe International Journal of Robotics Research 25 (9), 889-902

23 2006

Meta‐analysis of trials comparing ximelagatran with low molecularweight heparin for prevention of venous thromboembolism aftermajor orthopaedic surgeryAT Cohen, C Hirst, B Sherrill, P Holmes, D Fidan

23 2005


16 of 21 9/20/14 3:07 PM

Title Cited by Year

British journal of surgery 92 (11), 1335-1344

Motions and stability of a piecewise holonomic system: thediscrete Chaplygin sleighMJ Coleman, P HolmesRegular and chaotic dynamics 4 (2), 55-77

23 1999

Periodic, nonperiodic and irregular motions in a HamiltoniansystemP HolmesJOURNAL OF MATHEMATICS 10 (4)

23 1980

Reflexes and preflexes: on the role of sensory feedback onrhythmic patterns in insect locomotionJ Proctor, P HolmesBiological cybernetics 102 (6), 513-531

22 2010

Towards a factored analysis of legged locomotion modelsR Altendorfer, DE Koditschek, P HolmesRobotics and Automation, 2003. Proceedings. ICRA'03. IEEE International ...

22 2003

Heteroclinic cycles and modulated travelling waves in a systemwith< i> D</i>< sub> 4</sub> symmetryS Ann Campbell, P HolmesPhysica D: Nonlinear Phenomena 59 (1), 52-78

22 1992

The effect of modeled drag reduction on the wall regionN Aubry, JL Lumley, P HolmesTheoretical and Computational Fluid Dynamics 1 (4), 229-248

22 1990

Space-and time-periodic perturbations of the sine-GordonequationP HolmesDynamical Systems and Turbulence, Warwick 1980, 164-191

22 1981

On the derivation and tuning of phase oscillator models forlamprey central pattern generatorsPL Várkonyi, T Kiemel, K Hoffman, AH Cohen, P HolmesJournal of computational neuroscience 25 (2), 245-261

21 2008

Homoclinic explosions and implosionsA Doelman, P HolmesPhilosophical Transactions of the Royal Society of London. Series A ...

21 1996

Turbulence, Coherent StructuresG Berkooz, P Holmes, JL Lumley 21 1996


17 of 21 9/20/14 3:07 PM

Title Cited by Year

Dynamical Systems and Symmetry. Cambridge Monographs on Mechanics.Cambridge ...

Coherent structures in random media and waveletsG Berkooz, J Elezgaray, P HolmesPhysica D: Nonlinear Phenomena 61 (1), 47-58

21 1992

Bifurcation from O (2) symmetric heteroclinic cycles with threeinteracting modesSA Campbell, P HolmesNonlinearity 4 (3), 697

21 1991

Collective oscillations in the visual cortexDM Kammen, C Koch, PJ HolmesAdvances in neural information processing systems, 76-83

21 1990

Double Hopf bifurcation and quasi-periodic flow in a model forbaroclinic instabilityIM Moroz, P HolmesJournal of the Atmospheric Sciences 41 (21), 3147-3160

21 1984

Data analysis criteria and instrumentation requirements for thetransient measurement of mechanical impedancePJ Holmes, RG WhiteJournal of Sound and Vibration 25 (2), 217-243

21 1972

Spikes alone do not behavior make: why neuroscience needsbiomechanicsED Tytell, P Holmes, AH CohenCurrent opinion in neurobiology 21 (5), 816-822

20 2011

Local models of spatio-temporally complex fieldsH Dankowicz, P Holmes, G Berkooz, J ElezgarayPhysica D: Nonlinear Phenomena 90 (4), 387-407

20 1996

Stochastic analysis of wind-loaded structuresYK Lin, PJ HolmesJournal of the Engineering Mechanics Division 104 (2), 421-440

20 1978

Optimal performance in a countermanding saccade taskKF Wong-Lin, P Eckhoff, P Holmes, JD CohenBrain research 1318, 178-187

19 2010

Robust versus optimal strategies for two-alternative forced choicetasksM Zacksenhouse, R Bogacz, P Holmes

18 2010


18 of 21 9/20/14 3:07 PM

Title Cited by Year

Journal of mathematical psychology 54 (2), 230-246

Dynamical analysis of Bayesian inference models for the EriksentaskYS Liu, A Yu, P HolmesNeural computation 21 (6), 1520-1553

18 2009

On the dynamics of electrically-coupled neurons with inhibitorysynapsesJ Gao, P HolmesJournal of computational neuroscience 22 (1), 39-61

18 2007

Fundamental aspects of incompressible and compressibleturbulent flowsJL Lurnley, G Berkooz, J Elezgaray, P Holmes, A Poje, C VolteSimulation and Modeling of Turbulent Flows, 5

17 1996

Application of dynamical system theory to coherent structures inthe wall regionN Aubry, P Holmes, JL Lumley, E StonePhysica D: Nonlinear Phenomena 37 (1), 1-10

17 1989

Nonlinear oscillations and the smale horseshoe mapP HolmesChaos and Fractals: The Mathematics Behind the Computer Graphics, 25-39

17 1989

EEG oscillations reveal neural correlates of evidenceaccumulationMK Van Vugt, P Simen, LE Nystrom, P Holmes, JD CohenFrontiers in neuroscience 6

16 2012

Steering by transient destabilization in piecewise-holonomicmodels of legged locomotionJ Proctor, P HolmesRegular and Chaotic Dynamics 13 (4), 267-282

16 2008

Towards a neuromechanical model for insect locomotion: hybriddynamical systemsRM Ghigliazza, P HolmesRegular and Chaotic dynamics 10 (2), 193-225

16 2005

Euler buckling in a potential fieldP Holmes, G Domokos, G HekJournal of Nonlinear Science 10 (4), 477-505

16 2000


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Title Cited by Year

Wavelet projections of the Kuramoto-Sivashinsky equation I.Heteroclinic cycles and modulated traveling waves for shortsystemsM Myers, P Holmes, J Elezgaray, G BerkoozPhysica D: Nonlinear Phenomena 86 (3), 396-427

16 1995

Interaction of adjacent bursts in the wall regionBD Coller, P Holmes, JL LumleyPhysics of Fluids (1994-present) 6 (2), 954-961

16 1994

Knots and orbit genealogies in three dimensional flowsR Ghrist, P HolmesBifurcations and Periodic Orbits of Vector Fields, 185-239

16 1993

Nonlinear oscillationsAH Nayfeh, DT Mook, P HolmesJournal of Applied Mechanics 47, 692

16 1980

On a dynamical model for phase transformation in nonlinearelasticityWD Kalies, PJ HolmesFields Inst. Commun 5, 255-269

15 1996

The proper orthogonal decomposition, wavelets and modalapproaches to the dynamics of coherent structuresG Berkooz, J Elezgaray, P Holmes, J Lumley, A PojeApplied scientific research 53 (3-4), 321-338

15 1994

Heteroclinic cycles, exponential tails, and intermittency inturbulence productionP Holmes, E StoneStudies in Turbulence, 179-189

15 1992

Intersegmental coordination of cockroach locomotion: adaptivecontrol of centrally coupled pattern generator circuitsE Fuchs, P Holmes, T Kiemel, A AyaliFrontiers in neural circuits 4

14 2010

The Proper Orthogonal Decompositions in the Analysis ofTurbulent FlowsG Berkooz, P Holmes, JL LumleyAnnual Review of Fluid Mechanics 25, 537-537

14 1993

Bifurcations of dynamical systems and nonlinear oscillations inengineering systems 14 1978


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Title Cited by Year

PJ Holmes, JE MarsdenNonlinear partial differential equations and applications, 163-206

Dimension reduction and dynamics of a spiking neural networkmodel for decision making under neuromodulationP Eckhoff, KF Wong-Lin, P HolmesSIAM journal on applied dynamical systems 10 (1), 148-188

13 2011

A phase-reduced neuro-mechanical model for insect locomotion:feed-forward stability and proprioceptive feedbackJ Proctor, RP Kukillaya, P HolmesPhilosophical Transactions of the Royal Society A: Mathematical, Physical ...

13 2010

Buckling of extensible thermoelastic rodsJ Cisternas, P HolmesMathematical and computer modelling 36 (3), 233-243

13 2002

Homoclinic Saddle‐Node Bifurcations and Subshifts in a Three‐Dimensional FlowG Hek, A Doelman, P HolmesArchive for rational mechanics and analysis 145 (4), 291-329

13 1998

Reduction, stability, instability and bifurcation in rotationallysymmetric Hamiltonian systemsB Zombro, P HolmesDynamics and Stability of Systems 8 (1), 41-71

13 1993

Nonlinear dynamics, chaos, and mechanicsP HolmesApplied Mechanics Reviews 43 (5S), S23-S39

13 1990

A decision task in a social context: Human experiments, models,and analyses of behavioral dataA Nedic, D Tomlin, P Holmes, DA Prentice, JD CohenProceedings of the IEEE 100 (3), 713-733

12 2012

A simple decision task in a social context: Experiments, a model,and preliminary analyses of behavioral dataA Nedic, D Tomlin, P Holmes, DA Prentice, JD CohenDecision and Control, 2008. CDC 2008. 47th IEEE Conference on, 1115-1120

12 2008

Dates and citation counts are estimated and are determined automatically by a computerprogram.


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Documents

Philip Holmes - Google Scholar Citations · Chaos and fractals: The mathematics behind the computer graphics RL Devaney American Mathematical Soc. 118 1989 Cascades of homoclinic