John Guckenheimer, Ph.D. - Publications

Mathematics Cornell University, Ithaca, NY, United States 
Dynamical systems

100 high-probability publications. We are testing a new system for linking publications to authors. You can help! If you notice any inaccuracies, please sign in and mark papers as correct or incorrect matches. If you identify any major omissions or other inaccuracies in the publication list, please let us know.

Year Citation  Score
2015 Beatus T, Guckenheimer JM, Cohen I. Controlling roll perturbations in fruit flies. Journal of the Royal Society, Interface / the Royal Society. 12. PMID 25762650 DOI: 10.1098/rsif.2015.0075  1
2015 Maus HM, Revzen S, Guckenheimer J, Ludwig C, Reger J, Seyfarth A. Constructing predictive models of human running. Journal of the Royal Society, Interface / the Royal Society. 12. PMID 25505131 DOI: 10.1098/rsif.2014.0899  1
2015 Guckenheimer J, Lizarraga I. Shilnikov homoclinic bifurcation of mixed-mode oscillations Siam Journal On Applied Dynamical Systems. 14: 764-786. DOI: 10.1137/140972007  1
2015 Guckenheimer J, Krauskopf B, Osinga HM, Sandstede B. Invariant manifolds and global bifurcations Chaos. 25. DOI: 10.1063/1.4915528  1
2014 Iams S, Guckenheimer J. Flight stability of mosquitos: A reduced model Siam Journal On Applied Mathematics. 74: 1535-1550. DOI: 10.1137/140955513  1
2014 Guckenheimer J. From data to dynamical systems Nonlinearity. 27: R41-R50. DOI: 10.1088/0951-7715/27/7/R41  1
2013 Ristroph L, Ristroph G, Morozova S, Bergou AJ, Chang S, Guckenheimer J, Wang ZJ, Cohen I. Active and passive stabilization of body pitch in insect flight. Journal of the Royal Society, Interface / the Royal Society. 10: 20130237. PMID 23697713 DOI: 10.1098/rsif.2013.0237  1
2013 Guckenheimer J, Scheper C. Multiple time scale analysis of a model Belousov-Zhabotinskii reaction Siam Journal On Applied Dynamical Systems. 12: 1968-1996. DOI: 10.1137/130912840  1
2013 Guckenheimer J. A smooth multivariate interpolation algorithm Essays in Mathematics and Its Applications: in Honor of Stephen Smale's 80th Birthday. 231-239. DOI: 10.1007/978-3-642-28821-0_9  1
2013 Guckenheimer J. The birth of chaos Springer Proceedings in Mathematics and Statistics. 35: 3-24. DOI: 10.1007/978-3-0348-0451-6_1  1
2012 Revzen S, Guckenheimer JM. Finding the dimension of slow dynamics in a rhythmic system. Journal of the Royal Society, Interface / the Royal Society. 9: 957-71. PMID 21937489 DOI: 10.1098/rsif.2011.0431  1
2012 Guckenheimer J, Osinga HM. The singular limit of a hopf bifurcation Discrete and Continuous Dynamical Systems. 32: 2805-2823. DOI: 10.3934/dcds.2012.32.2805  1
2012 Guckenheimer J, Johnson T, Meerkamp P. Rigorous enclosures of a slow manifold Siam Journal On Applied Dynamical Systems. 11: 831-863. DOI: 10.1137/120861813  1
2012 Desroches M, Guckenheimer J, Krauskop B, Kuehn C, Osinga HM, Wechselberger M. Mixed-mode oscillations with multiple time scales Siam Review. 54: 211-288. DOI: 10.1137/100791233  1
2011 Ristroph L, Bergou AJ, Guckenheimer J, Wang ZJ, Cohen I. Paddling mode of forward flight in insects. Physical Review Letters. 106: 178103. PMID 21635066 DOI: 10.1103/PhysRevLett.106.178103  1
2011 Sherwood WE, Harris-Warrick R, Guckenheimer J. Synaptic patterning of left-right alternation in a computational model of the rodent hindlimb central pattern generator. Journal of Computational Neuroscience. 30: 323-60. PMID 20644988 DOI: 10.1007/s10827-010-0259-y  1
2011 Guckenheimer J, Scheper C. A geometric model for mixed-mode oscillations in a chemical system? Siam Journal On Applied Dynamical Systems. 10: 92-128. DOI: 10.1137/100801950  1
2011 Ellner SP, Guckenheimer J. Dynamic models in biology Dynamic Models in Biology. 1-329.  1
2010 Bergou AJ, Ristroph L, Guckenheimer J, Cohen I, Wang ZJ. Fruit flies modulate passive wing pitching to generate in-flight turns. Physical Review Letters. 104: 148101. PMID 20481964 DOI: 10.1103/PhysRevLett.104.148101  1
2010 Ristroph L, Bergou AJ, Ristroph G, Coumes K, Berman GJ, Guckenheimer J, Wang ZJ, Cohen I. Discovering the flight autostabilizer of fruit flies by inducing aerial stumbles. Proceedings of the National Academy of Sciences of the United States of America. 107: 4820-4. PMID 20194789 DOI: 10.1073/pnas.1000615107  1
2010 Sherwood WE, Guckenheimer J. Dissecting the phase response of a model bursting neuron Siam Journal On Applied Dynamical Systems. 9: 659-703. DOI: 10.1137/090773519  1
2009 Carver SG, Cowan NJ, Guckenheimer JM. Lateral stability of the spring-mass hopper suggests a two-step control strategy for running. Chaos (Woodbury, N.Y.). 19: 026106. PMID 19566266 DOI: 10.1063/1.3127577  1
2009 Guckenheimer J, Kuehn C. Homoclinic orbits of the fitzhugh-nagumo equation: The singular-limit Discrete and Continuous Dynamical Systems - Series S. 2: 851-872. DOI: 10.3934/dcdss.2009.2.851  1
2009 Guckenheimer J, Kuehn C. Computing slow manifolds of saddle type* Siam Journal On Applied Dynamical Systems. 8: 854-879. DOI: 10.1137/080741999  1
2009 Cao X, Guckenheimer J, Saloff-Coste L. The backward behavior of the Ricci and cross-curvature flows on SL(2,ℝ) Communications in Analysis and Geometry. 17: 777-796.  1
2008 Revzen S, Guckenheimer JM. Estimating the phase of synchronized oscillators. Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics. 78: 051907. PMID 19113155 DOI: 10.1103/PhysRevE.78.051907  1
2008 Guckenheimer J. Return maps of folded nodes and folded saddle-nodes. Chaos (Woodbury, N.Y.). 18: 015108. PMID 18377089 DOI: 10.1063/1.2790372  1
2008 Clewley RH, Guckenheimer JM, Valero-Cuevas FJ. Estimating effective degrees of freedom in motor systems. Ieee Transactions On Bio-Medical Engineering. 55: 430-42. PMID 18269978 DOI: 10.1109/TBME.2007.903712  1
2008 Tien JH, Guckenheimer J. Parameter estimation for bursting neural models. Journal of Computational Neuroscience. 24: 358-73. PMID 17999167 DOI: 10.1007/s10827-007-0060-8  1
2008 Guckenheimer J. Singular Hopf bifurcation in systems with two slow variables Siam Journal On Applied Dynamical Systems. 7: 1355-1377. DOI: 10.1137/080718528  1
2007 Venkadesan M, Guckenheimer J, Valero-Cuevas FJ. Manipulating the edge of instability. Journal of Biomechanics. 40: 1653-61. PMID 17400231 DOI: 10.1016/j.jbiomech.2007.01.022  1
2007 Ren Z, Pope SB, Vladimirsky A, Guckenheimer JM. Application of the ICE-PIC method for the dimension reduction of chemical kinetics coupled with transport Proceedings of the Combustion Institute. 31: 473-481. DOI: 10.1016/j.proci.2006.07.106  1
2007 Guckenheimer J, Lamar MD. Periodic orbit continuation in multiple time scale systems Numerical Continuation Methods For Dynamical Systems: Path Following and Boundary Value Problems. 253-267. DOI: 10.1007/978-1-4020-6356-5_8  1
2006 Ren Z, Pope SB, Vladimirsky A, Guckenheimer JM. The invariant constrained equilibrium edge preimage curve method for the dimension reduction of chemical kinetics. The Journal of Chemical Physics. 124: 114111. PMID 16555878 DOI: 10.1063/1.2177243  1
2006 Holmes P, Full RJ, Koditschek D, Guckenheimer J. The dynamics of legged locomotion: Models, analyses, and challenges Siam Review. 48: 207-304. DOI: 10.1137/S0036144504445133  1
2006 Guckenheimer J, Wechselberger M, Young LS. Chaotic attractors of relaxation oscillators Nonlinearity. 19: 701-720. DOI: 10.1088/0951-7715/19/3/009  1
2006 Phipps E, Casey R, Guckenheimer J. Periodic Orbits of Hybrid Systems and Parameter Estimation via AD Lecture Notes in Computational Science and Engineering. 50: 211-223. DOI: 10.1007/3-540-28438-9_19  1
2005 MacLean JN, Zhang Y, Goeritz ML, Casey R, Oliva R, Guckenheimer J, Harris-Warrick RM. Activity-independent coregulation of IA and Ih in rhythmically active neurons. Journal of Neurophysiology. 94: 3601-17. PMID 16049145 DOI: 10.1152/jn.00281.2005  1
2005 Gruhn M, Guckenheimer J, Land B, Harris-Warrick RM. Dopamine modulation of two delayed rectifier potassium currents in a small neural network. Journal of Neurophysiology. 94: 2888-900. PMID 16014791 DOI: 10.1152/jn.00434.2005  1
2005 Guckenheimer J, Hoffman K, Weckesser W. Bifurcations of relaxation oscillations near folded saddles International Journal of Bifurcation and Chaos in Applied Sciences and Engineering. 15: 3411-3421. DOI: 10.1142/S0218127405014131  1
2005 Krauskopf B, Osinga HM, Doedel EJ, Henderson ME, Guckenheimer J, Vladimirsky A, Dellnitz M, Junge O. A survey of methods for computing (UN)stable manifolds of vector fields International Journal of Bifurcation and Chaos in Applied Sciences and Engineering. 15: 763-791. DOI: 10.1142/S0218127405012533  1
2004 Robertson SS, Guckenheimer J, Masnick AM, Bacher LF. The dynamics of infant visual foraging. Developmental Science. 7: 194-200. PMID 15320379 DOI: 10.1111/j.1467-7687.2004.00338.x  1
2004 Guckenheimer J, Vladimirsky A. A fast method for approximating invariant manifolds Siam Journal On Applied Dynamical Systems. 3: 232-260. DOI: 10.1137/030600179  1
2003 Zhang Y, Oliva R, Gisselmann G, Hatt H, Guckenheimer J, Harris-Warrick RM. Overexpression of a hyperpolarization-activated cation current (Ih) channel gene modifies the firing activity of identified motor neurons in a small neural network. The Journal of Neuroscience : the Official Journal of the Society For Neuroscience. 23: 9059-67. PMID 14534239  1
2003 Bold K, Edwards C, Guckenheimer J, Guharay S, Hoffman K, Hubbard J, Oliva R, Weckesser W. The forced van der Pol equation II: Canards in the reduced system Siam Journal On Applied Dynamical Systems. 2: 570-608. DOI: 10.1137/S1111111102419130  1
2003 Guckenheimer J, Hoffman K, Weckesser W. The forced van der Pol equation I: The slow flow and its bifurcations Siam Journal On Applied Dynamical Systems. 2.  1
2002 Guckenheimer J. Chapter 8 Numerical analysis of dynamical systems Handbook of Dynamical Systems. 2: 345-390. DOI: 10.1016/S1874-575X(02)80029-7  1
2002 Guckenheimer J, Oliva RA. Chaos in the hodgkio-hoxley model Siam Journal On Applied Dynamical Systems. 1: 105-114.  1
2001 Guckenheimer J, Meloon B. Computing periodic orbits and their bifurcations with automatic differentiation Siam Journal On Scientific Computing. 22: 951-985. DOI: 10.1137/S1064827599359278  1
2000 Guckenheimer J, Hoffman K, Weckesser W. Numerical computation of canards International Journal of Bifurcation and Chaos in Applied Sciences and Engineering. 10: 2669-2687.  1
2000 Guckenheimer J, Willms AR. Asymptotic analysis of subcritical Hopf-homoclinic bifurcation Physica D: Nonlinear Phenomena. 139: 195-216.  1
1999 Willms AR, Baro DJ, Harris-Warrick RM, Guckenheimer J. An improved parameter estimation method for Hodgkin-Huxley models. Journal of Computational Neuroscience. 6: 145-68. PMID 10333160 DOI: 10.1023/A:1008880518515  1
1999 Choe WG, Guckenheimer J. Computing periodic orbits with high accuracy Computer Methods in Applied Mechanics and Engineering. 170: 331-341.  1
1997 Guckenheimer J, Harris-Warrick R, Peck J, Willms A. Bifurcation, bursting, and spike frequency adaptation. Journal of Computational Neuroscience. 4: 257-77. PMID 9257235 DOI: 10.1023/A:1008871803040  1
1997 Govaerts W, Guckenheimer J, Khibnik A. Defining functions for multiple hopf bifurcations Siam Journal On Numerical Analysis. 34: 1269-1288.  1
1997 Guckenheimer J, Myers M, Sturmfels B. Computing hopf bifurcations I Siam Journal On Numerical Analysis. 34: 1-21.  1
1996 Guckenheimer J, Malo S. Computer-generated proofs of phase portraits for planar systems International Journal of Bifurcation and Chaos in Applied Sciences and Engineering. 6: 889-892. DOI: 10.1142/S0218127496000497  1
1996 Guckenheimer J, Myers M. Computing hopf bifurcations II: Three examples from neurophysiology Siam Journal On Scientific Computing. 17: 1275-1301.  1
1995 Harris-Warrick RM, Coniglio LM, Levini RM, Gueron S, Guckenheimer J. Dopamine modulation of two subthreshold currents produces phase shifts in activity of an identified motoneuron. Journal of Neurophysiology. 74: 1404-20. PMID 8989381  1
1995 Harris-Warrick RM, Coniglio LM, Barazangi N, Guckenheimer J, Gueron S. Dopamine modulation of transient potassium current evokes phase shifts in a central pattern generator network. The Journal of Neuroscience : the Official Journal of the Society For Neuroscience. 15: 342-58. PMID 7823140  1
1995 Guckenheimer J. A Robust Hybrid Stabilization Strategy for Equilibria Ieee Transactions On Automatic Control. 40: 321-326. DOI: 10.1109/9.341802  1
1995 Guckenheimer J. Phase portraits of planar vector fields: Computer proofs Experimental Mathematics. 4: 153-165. DOI: 10.1080/10586458.1995.10504316  1
1995 Guckenheimer J. Dynamical systems theory for ecologists: a brief overview Ecological Time Series. 54-69.  1
1994 Doedel EJ, Friedman MJ, Guckenheimer J. Computing connecting orbits: general algorithm and applications to the sine-Gordon and Hodgkin-Huxley equations Ieice Transactions On Fundamentals of Electronics, Communications and Computer Sciences. 1801-1805.  1
1993 Guckenheimer J, Gueron S, Harris-Warrick RM. Mapping the dynamics of a bursting neuron. Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences. 341: 345-59. PMID 7504823 DOI: 10.1098/rstb.1993.0121  1
1993 Guckenheimer J, Labouriau JS. Bifurcation of the Hodgkin and Huxley equations: A new twist Bulletin of Mathematical Biology. 55: 937-952. DOI: 10.1007/BF02460693  1
1993 Golomb D, Guckenheimer J, Gueron S. Reduction of a channel-based model for a stomatogastric ganglion LP neuron Biological Cybernetics. 69: 129-137. DOI: 10.1007/BF00226196  1
1992 Guckenheimer J, Mahalov A. Instability induced by symmetry reduction. Physical Review Letters. 68: 2257-2260. PMID 10045349 DOI: 10.1103/PhysRevLett.68.2257  1
1992 Guckenheimer J, Worfolk P. Instant chaos Nonlinearity. 5: 1211-1222. DOI: 10.1088/0951-7715/5/6/001  1
1992 Guckenheimer J, Mahalov A. Resonant triad interactions in symmetric systems Physica D: Nonlinear Phenomena. 54: 267-310. DOI: 10.1016/0167-2789(92)90040-T  1
1992 Guckenheimer J. Symmetry properties of confined convective states Zamp Zeitschrift FüR Angewandte Mathematik Und Physik. 43: 422-429. DOI: 10.1007/BF00946238  1
1991 Baesens C, Guckenheimer J, Kim S, MacKay RS. Three coupled oscillators: mode-locking, global bifurcations and toroidal chaos Physica D: Nonlinear Phenomena. 49: 387-475. DOI: 10.1016/0167-2789(91)90155-3  1
1989 Guckenheimer J, Rand R, Schlomiuk D. Degenerate homoclinic cycles in perturbations of quadratic Hamiltonian systems Nonlinearity. 2: 405-418. DOI: 10.1088/0951-7715/2/3/002  1
1989 Kim S, MacKay RS, Guckenheimer J. Resonance regions for families of torus maps Nonlinearity. 2: 391-404. DOI: 10.1088/0951-7715/2/3/001  1
1989 Armbruster D, Guckenheimer J, Kim S. Chaotic dynamics in systems with square symmetry Physics Letters A. 140: 416-420. DOI: 10.1016/0375-9601(89)90078-9  1
1988 Armbruster D, Guckenheimer J, Holmes P. Heteroclinic cycles and modulated travelling waves in systems with O(2) symmetry Physica D: Nonlinear Phenomena. 29: 257-282. DOI: 10.1016/0167-2789(88)90032-2  1
1987 Guckenheimer J. Limit sets of S-unimodal maps with zero entropy Communications in Mathematical Physics. 110: 655-659. DOI: 10.1007/BF01205554  1
1987 Dangelmayr G, Guckenheimer J. On a four parameter family of planar vector fields Archive For Rational Mechanics and Analysis. 97: 321-352. DOI: 10.1007/BF00280410  1
1986 Cho HM, Tycko R, Pines A, Guckenheimer J. Iterative maps for bistable excitation of two-level systems. Physical Review Letters. 56: 1905-1908. PMID 10032807 DOI: 10.1103/PhysRevLett.56.1905  1
1986 Guckenheimer J. Multiple bifurcation problems for chemical reactors Physica D: Nonlinear Phenomena. 21: 1-20. DOI: 10.1016/0167-2789(86)90093-X  1
1986 Guckenheimer J. MATHEMATICS OF CHAOS Engineering: Cornell Quarterly. 20: 36-41.  1
1986 Guckenheimer J. STRANGE ATTRACTORS IN FLUIDS: ANOTHER VIEW Annual Review of Fluid Mechanics. 1: 15-31.  1
1985 Tycko R, Pines A, Guckenheimer J. Fixed point theory of iterative excitation schemes in NMR The Journal of Chemical Physics. 83: 2775-2802.  1
1983 Guckenheimer J. Toolkit for Nonlinear Dynamics Ieee Transactions On Circuits and Systems. 30: 586-590. DOI: 10.1109/TCS.1983.1085393  1
1983 Guckenheimer J, Buzyna G. Dimension measurements for geostrophic turbulence Physical Review Letters. 51: 1438-1441. DOI: 10.1103/PhysRevLett.51.1438  1
1983 Knobloch E, Guckenheimer J. Convective transitions induced by a varying aspect ratio Physical Review A. 27: 408-417. DOI: 10.1103/PhysRevA.27.408  1
1983 Guckenheimer J, Knobloch E. Nonlinear Convection in a Rotating Layer: Amplitude Expansions and Normal Forms Geophysical & Astrophysical Fluid Dynamics. 23: 247-272. DOI: 10.1080/03091928308209045  1
1983 Guckenheimer J. Persistent properties of bifurcations Physica D: Nonlinear Phenomena. 7: 105-110. DOI: 10.1016/0167-2789(83)90120-3  1
1982 Guckenheimer J. Noise in chaotic systems Nature. 298: 358-361. DOI: 10.1038/298358a0  1
1980 Guckenheimer J. Symbolic dynamics and relaxation oscillations Physica D: Nonlinear Phenomena. 1: 227-235. DOI: 10.1016/0167-2789(80)90014-7  1
1980 Guckenheimer J. DYNAMICS OF THE VAN DER POL EQUATION Ieee Transactions On Circuits and Systems. 983-989.  1
1979 Guckenheimer J, Williams RF. Structural stability of Lorenz attractors Publications MathéMatiques De L'Institut Des Hautes Scientifiques. 50: 59-72. DOI: 10.1007/BF02684769  1
1979 Guckenheimer J. Sensitive dependence to initial conditions for one dimensional maps Communications in Mathematical Physics. 70: 133-160. DOI: 10.1007/BF01982351  1
1978 Auslander D, Guckenheimer J, Oster G. Random evolutionarily stable strategies. Theoretical Population Biology. 13: 276-93. PMID 694787 DOI: 10.1016/0040-5809(78)90047-3  1
1978 Guckenheimer J. The catastrophe controversy The Mathematical Intelligencer. 1: 15-20. DOI: 10.1007/BF03023037  1
1977 Guckenheimer J, Oster G, Ipaktchi A. The dynamics of density dependent population models. Journal of Mathematical Biology. 4: 8-147. PMID 886232 DOI: 10.1007/BF00275980  1
1977 Guckenheimer J. In support of catastrophe theory [5] Nature. 270: 383-384. DOI: 10.1038/270383a0  1
1977 Guckenheimer J. On the bifurcation of maps of the interval Inventiones Mathematicae. 39: 165-178. DOI: 10.1007/BF01390107  1
1975 Guckenheimer J. Isochrons and phaseless sets Journal of Mathematical Biology. 1: 259-273. DOI: 10.1007/BF01273747  1
1975 Guckenheimer J. Shocks and rarefactions in two space dimensions Archive For Rational Mechanics and Analysis. 59: 281-291. DOI: 10.1007/BF00251604  1
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