Publications

  • J. Guckenheimer, Endomorphisms of the Riemann sphere, Proc. Am. Math. Soc. Symposia in Pure Math. XIV, 95-124, 1970. 
  • J. Guckenheimer, Holomorphic vector fields on CP(2), An. Acad. Brasil. Cienc. 42, 415-420, 1970. 
  • J. Guckenheimer, Axiom A + No Cycles implies zeta(f) rational. Bulletin Am. Math. Soc. 76, 592-594, 1970. 
  • J. Guckenheimer, Hartman's theorem for complex flows in the Poincare domain. Compositio, 24, 75-82, 1972. 
  • J. Guckenheimer, Absolutely omega-stable diffeomorphisms, Topology 11, 195-197, 1972. 
  • J. Guckenheimer, Bifurcation and catastrophe, Dynamical Systems, ed. M.M. Peixoto, Academic Press, 99-110, 1973. 
  • J. Guckenheimer, One parameter families of vector fields: another non-density theorem, Dynamical Systems, ed. M.M. Peixoto, Academic Press, 111-128, 1973. 
  • J. Guckenheimer, Catastrophes and partial differential equations. Annales de l'Institut Fourier 23, 31-59, 1973. 
  • J. Guckenheimer, Review of Stabilite Structurelle et Morphogenese by Rene Thom, Bulletin Am. Math. Soc. 79, 878-890, 1973. 
  • J. Guckenheimer, Caustics, Global Analysis and Its Applications II, International Atomic Energy Agency, 281-289, 1974. 
  • J. Guckenheimer, Caustics and non-degenerate hamiltonians, Topology 13, 127-133, 1974. 
  • J. Guckenheimer, Solving a single conservation law, Lecture Notes in Mathematics, 468, 108-134, 1974. 
  • J. Guckenheimer, Isochrons and phaseless sets, J. Math. Biology 1, 259-273, 1975. 
  • J. Guckenheimer, Shocks and rarefactions in two space dimensions, Arch. Rat. Mech. Anal. 59, 281-291, 1975. 
  • G. Oster and J. Guckenheimer, Bifurcation phenomena in population models, in The Hopf Bifurcation Theorem and its Applications, ed. J. Marsden and M. McCracken, Springer-Verlag, 327-353, 1976. 
  • J. Guckenheimer, A strange, strange attractor, in The Hopf Bifurcation Theorem and its Applications, ed. J. Marsden and M. McCracken, Springer-Verlag, 368-381, 1976. 
  • J. Guckenheimer, Constant velocity waves in oscillating chemical reactions, Lecture Notes in Mathematics, 525, 99-103, 1976. 
  • J. Guckenheimer, G. Oster and A. Ipaktchi, Dynamics of deterministic population models, J. Math. Biology 4, 101-147, 1977. 
  • J. Guckenheimer, The cusps of Zeeman's catastrophe machine, Topology 16, 177-180, 1977. 
  • J. Guckenheimer, On the bifurcation of maps of the interval, Inventiones Math. 39, 165-178, 1977. 
  • D. Auslander, J. Guckenheimer and G. Oster, Random evolutionarily stable strategies, J. Theoretical Population Biology 13, 276-293, 1978. 
  • J. Guckenheimer, Comments on catastrophe and chaos, Some Mathematical Questions in Biology IX, Am. Math. Soc. 1-48, 1978.  
  • J. Guckenheimer, The catastrophe controversy, Mathematical Intelligencer 1, 15-20, 1978. 
  • J. Guckenheimer and R. F. Williams, Structural stability of Lorenz attractors, Publ. I. H. E. S. 50, 60-72, 1979. 
  • J. Guckenheimer, The bifurcation of quadratic functions, Annals. N.Y. Acad. Sci. 316, 78-85, 1979. 
  • J. Guckenheimer, A brief introduction to dynamical systems, Lectures in Appl. Math. 17, 187-253, 1979. 
  • J. Guckenheimer, Sensitive dependence to initial conditions for one dimensional maps, Comm. Math. Phys. 70, 133-160, 1979.
  •  J. Guckenheimer, One dimensional dynamics, Annals N. Y. Acad. Sci. 316, 76-85, 1979. 
  • J. Guckenheimer, J. Moser and S. Newhouse, Dynamical Systems, CIME Lectures, Birkhauser, 289pp., 1980. 
  •  J. Guckenheimer, Instabilities and chaos in nonhydrodynamic systems, in Hydrodynamic Instabilities and the Transition to Turbulence, ed. H. L. Swinney, Springer-Verlag, 271-287, 1980. 
  • J. Guckenheimer, Symbolic dynamics and relaxation oscillations, Physica D1, 227-235, 1980. 
  • J. Guckenheimer, Growth of topological entropy for one dimensional maps, Lecture Notes in Mathematics 819, 216-223, 1980. 
  • L. Block, J. Guckenheimer, M. Misiurewicz and Lai Sang Young, Periodic points of one dimensional maps, Lecture Notes in Mathematics 819, 18-34, 1980. 
  • J. Guckenheimer, Patterns of bifurcation, New Approaches to Nonlinear Problems in Dynamics, ed. P. Holmes, SIAM, 71-104, 1980. 
  • J. Guckenheimer, Dynamics of the van der Pol equation, IEEE Trans. Circuits and Systems 27, 983-989, 1980. 
  • J. Guckenheimer, On a codimension two bifurcation, Lecture Notes in Mathematics 898, 99-142, 1981. 
  • J. Guckenheimer, Noise in chaotic systems, Nature 298, 358-361, 1982. 
  • J. Guckenheimer and E. Knobloch, Nonlinear convection in a rotating layer: amplitude expansions and normal forms, Geophys. Astrophys. Fluid Dynamics 23, 247-272, 1983. 
  • E. Knobloch and J. Guckenheimer, Convective transitions induced by varying aspect ratio, Phys. Rev. A27, 408-417, 1983. 
  • J. Guckenheimer, An introduction to chaotic motion and strange attractors, Lectures in Appl. Math. 20, 220-227, 1983. 
  • J. Guckenheimer, Persistent properties of bifurcations, Physica D7, 105-110, 1983. 
  • J. Guckenheimer, Strange attractors in fluid dynamics, Lecture Notes in Physics 179, 149-157, 1983. 
  • J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcation of Vector Fields, Springer-Verlag, 453pp., 1983. 
  • J. Guckenheimer, Toolkit for nonlinear dynamics, IEEE Trans. Circuits and Systems 30, 586-590, 1983. 
  • J. Guckenheimer and G. Buzyna, Dimension measurements for geostrophic turbulence, Phys. Rev. Lett. 51, 1438-1441, 1983. 
  • J. Guckenheimer, Multiple bifurcations of codimension two, SIAM J. Math. Anal. 15, 1-49, 1984. 
  • J. Guckenheimer, Dimension estimates for attractors, Contemporary Mathematics 28, 357-367, 1984. 
  • J. Guckenheimer and R. McGehee, A proof of the Mandelbrot N-squared conjecture, Mittag-Leffler Institute Report 15, 12pp., 1984. 
  • R. Tycko, A. Pines and J. Guckenheimer, Fixed point theory of iterative excitation schemes in NMR, J. Chem. Phys. 83, 2775-2802, 1985. 
  • J. Guckenheimer, Multiple bifurcation problems for chemical reactors, Physica 20D, 1-20, 1986. 
  • J. Guckenheimer, Global Bifurcations in simple models of a chemical reactor, Lectures in Applied Mathematics, 24, 163-174, 1986. 
  • J. Guckenheimer, A codimension two bifurcation with circular symmetry, Contemporary Mathematics, 56, 175-184, 1986. 
  • J. Guckenheimer, M. Golubitsky and J. Guckenheimer, eds., Multiparameter Bifurcation Theory, Contemporary Mathematics 56, American Mathematical Society, xvii + 387 pp., 1986. 
  • J. Guckenheimer, H. Cho, R. Tycko, A. Pines, and J. Guckenheimer, Iterative maps for bistable excitation of two-level systems, Phys. Rev. Lett. 56, 1905-1908, 1986. 
  • J. Guckenheimer, Strange attractors in fluids: another view, Ann. Rev. Fluid Mech., 18, 15-31, 1986. 
  • G. Dangelmayr and J. Guckenheimer, On a four parameter family of planar vector fields, Arch. Rat. Mech. Anal., 97, 321-352, 1987. 
  • J. Guckenheimer, Renormalization of one dimensional mappings and strange attractors, Contemporary Mathematics 58 part III, 143--160, 1987. 
  • J. Guckenheimer, Limit Sets of S-unimodal maps with zero entropy, Comm. Math. Phys. 110, 655--659, 1987. 
  • J. Guckenheimer, Comments on multiple bifurcations, Proceedings of 1986 Army Research Conference. 
  • J. Guckenheimer and P. Holmes, Structurally stable heteroclinic cycles, Proc. Camb. Phil. Soc. 103, 189--192, 1988. 
  • Dieter Armbruster, J. Guckenheimer and P. Holmes, Heteroclinic cycles and modulated travelling waves in systems with O(2) symmetry, Physica D29, 257--282, 1988. 
  • J. Guckenheimer, R. Rand and D. Schlomiuk, Degenerate homoclinic cycles in perturbations of quadratic hamiltonian systems, Nonlinearity, 2, 405--418, 1989. 
  • Dieter Armbruster, J. Guckenheimer and P. Holmes, Kuramoto-Sivashinsky Dynamics on the center-unstable manifold, SIAM J. Appl. Math, 49, 676--691, 1989. 
  • J. Guckenheimer, Obstacles to modelling large dynamical systems, Mathematical Approaches to Problems in Resource Management and Ecology, C. Chavez et al., ed. Lecture Notes in Mathematical Biology 81, 319--327, 1989. 
  • S. Kim, R. MacKay and John Guckenheimer, Resonance regions for families of torus maps, Nonlinearity, 2, 391--404, 1989. 
  • D. Armbruster, J. Guckenheimer and S. Kim, Chaotic Dynamics in Systems with Square Symmetry, Physics Letters A, 140, 416--420, 1989. 
  • S. Kim, J. Guckenheimer, FunTorus, interactive explorations of the two dimensional torus, MSI Technical Report, 1989. 
  • J. Guckenheimer and S. Johnson, Distortion of S-unimodal maps, Annals of Mathematics, 132, 71--130, 1990. 
  • J. Guckenheimer, R. Rand and D. Schlomiuk, Integrability of plane quadratic vector fields, Expositiones Mathematicae, 8, 3--25, 1990. 
  • S. Kim and J. Guckenheimer, The two dimensional torus: Numerical explorations and mathematical conjectures, Chaos/XAOC Soviet-American Perspectives on Nonlinear Science, AIP, 145--152, 1990. 
  • G. Berkooz, J. Guckenheimer, P. Holmes, J. Lumley, J. Marsden, N. Aubry and E. Stone, Dynamical Systems Theory Approach to the Wall Region, AIAA Fluid Dynamics, Plasma Dynamics and Lasers Conference, 1990. 
  • J. Guckenheimer and S. Kim, kaos, Dynamical System Toolkit with Interactive Graphic Interface, MSI Technical report, 1990. 
  • C. Baesens, J. Guckenheimer, S. Kim and R. MacKay, Simple Resonance Regions of Torus Diffeomorphisms, Patterns and Dynamics of Reactive Media (Aris, Aronson & Swinney eds.), IMA Volumes in Mathematics and its Applications, 37, 1--11, 1991. 
  • C. Baesens, J. Guckenheimer, S. Kim and R. MacKay, Three Coupled Oscillators: Mode-locking, Global Bifurcations and Toroidal Chaos, Physica D, 49, 387--485, 1991. 
  • D. Armbruster, J. Guckenheimer, and S. Kim, Resonant Surface Waves in a Square Container, Differential Equations and Computer Algebra, M. Singer, ed., Academic Press, 61--76, 1991. 
  • J. Guckenheimer, Computational Environments for Exploring Dynamical Systems, Int., Journal of Bifurcation and Chaos, 1, 269--276, 1991. 
  • J. Guckenheimer, Symmetry Properties of Confined Convective States, Z. angew Math Phys, 43, 422--429, 1992. 
  • A. Back, J. Guckenheimer, and M. Myers, A Dynamical Simulation Facility for Hybrid Systems, MSI Technical Report 92-6, 1992. 
  • J. Guckenheimer, Chaos: Science or Non-science, Nonlinear Science Today, 1(2), 6-8, 1992. 
  • J. Guckenheimer and A. Mahalov, Resonant Triad Interactions in Systems with O(2) Symmetry, Physica D, 54, 267--310, 1992. 
  • J. Guckenheimer, A. Back, J. Guckenheimer, M. Myers, F. Wicklin and P. Worfolk, dstool: Computer Assisted Exploration of Dynamical Systems, Notices of the American Mathemtical Society, 39, 303--309, 1992. 
  • J. Guckenheimer and A. Mahalov, Instability induced by symmetry reduction, Phys. Rev. Lett., 68, 2257--2260, 1992. 
  • J. Guckenheimer and P. Worfolk, Instant Chaos, Nonlinearity 5, 1211--1222, 1992. 
  • J. Guckenheimer and I. Labouriau, Bifurcation of the Hodgkin Huxley Equations: A New Twist, Bulletin of Math. Biol., 55, 937--952, 1993. 
  • D. Golomb, J. Guckenheimer, and S. Gueron, Reduction of a Channel Based Model for a Stomatogastric Ganglion LP Neuron, Biol. Cybernetics, 69, 129--137, 1993. 
  • J. Guckenheimer and P. Worfolk, Dynamical Systems: Some Computational Problems, in Bifurcations and Periodic Orbits of Vector Fields, D. Schlomiuk, ed. pp241-278, Kluwer 1993. 
  • J. Guckenheimer, S. Gueron and R. Harris-Warrick, The Dynamics of a Conditionally Bursting Neuron, Philosophical Transactions of Royal Society, 341, 345-359, 1993. 
  • J. Guckenheimer and S. Johnson, Beyond Hyperbolicity: Expansion Properties of One Dimensional Mappings,in From Topology to Computation, Hirsch, Marsden and Shub, editors, 227-236, Springer-Verlag, 1993. 
  • E. J. Doedel, M. J. Friedman and J. Guckenheimer, On computing connecting orbits in the Sine-Gordon and Hodgkin-Huxley equations, IEICE Trans. fundamentals, E77-A, 1-4, 1994. 
  • J. Guckenheimer, The role of geometry in computational dynamics, Dynamics, Bifurcation and Symmetry, P. Chossat, ed. 159-166, 1994. 
  • J. Guckenheimer, A general review of dynamical systems, in Ecological Time Series, T. Powell and J. Steele, eds., Chapman-Hall, 54-69, 1994. 
  • J. Guckenheimer, R. Harris-Warrick, L. Coniglio, N. Barazangi, J. Guckenheimer and S. Gueron, Dopamine modulation of transient potassium current evokes phase shifts in a central pattern generator network, J. Neuroscience, 15, 342-358, 1995. 
  • J. Guckenheimer, A Robust Hybrid Stabilization Strategy for Equilibria, IEEE Trans. Automatic Control, 40, 321-326, 1995. 
  •  J. Guckenheimer, Phase portraits of planar vector fields: computer proofs, J. Experimental Mathematics, 4, 153-164, 1995. 
  • J. Guckenheimer and S. Johnson, Planar hybrid systems, Hybrid Systems II, Lecture Notes in Computer Science, 999, 202-225, 1995. 
  • J. Guckenheimer, R. Harris-Warrick, L. Coniglio, R. Levini, S. Gueron and J. Guckenheimer, Dopamine modulation of two subthreshold currents produces phase shifts in activity of an identified neuron, J. Neurophysiology, 74, 1404-1420, 1995. 
  • J. Guckenheimer, Phase portraits of planar vector fields: computer proofs, J. Experimental Math., 4, 153-165, 1995.  
  • J. Guckenheimer and S. Malo, Computer-generated Proofs of Phase Portraits for Planar Systems, , Int. J. Bif. and Chaos, 6, 889-892, 1996. 
  •  J. Guckenheimer, and M. Myers, Computing Hopf Bifurcations II, SIAM J. Sci. Comp, 17, 1275-1301, 1996. 
  •  J. Guckenheimer, Numerical analysis of dynamical systems, in Chaotic, Fractal and Nonlinear Signal Processing, R. Katz ed., AIP Press, 3-13, 1996. 
  • J. Guckenheimer, Towards a global theory of singularly perturbed systems, Progress in Nonlinear Differential Equations and Their Applications, 19, 214-225, 1996. 
  • J. Guckenheimer, M. Myers and B. Sturmfels, Computing Hopf Bifurcations I, SIAM J. Num. Anal., 34, 1-21, 1997.
  • W. Govaerts, J. Guckenheimer and A. Khibnik, Defining functions for multiple Hopf bifurcations, SIAM J. Num. Anal., 34, 1269-1288, 1997. 
  • J. Guckenheimer and P. Rowat, Dynamical systems analyses of real neuronal networks, in Neurons, Networks nad Motor Behavior, P. Stein, S. Grillner and A. Seleverston, eds., MIT Press, 151-163, 1997.
  • J. Guckenheimer, R. Harris-Warrick, J. Peck and A. Willms, Bifurcation, bursting and spike frequency adaptation, J Comput Neurosci. 4(3):257-77, 1997.
  • J. Guckenheimer, Book Review: Dynamical Systems and Numerical Analysis by Stuart and Humphries, Ergodic Theory and Dynamical Systems, 18, 759-763, 1998.
  • J. Guckenheimer, Computer simulation and beyond - for the 21st Century, Notices of the Am. Math. Soc. 45, 1120-1123, 1998.
  • A. R. Willms, D. J. Baro, R. M. Harris-Warrick and J. Guckenheimer,An improved parameter estimation method for Hodgkin-Huxley models, J. Comp. Neuroscience, 6, 145-168, 1999.
  • J. Guckenheimer, SIAM Past President's Address, SIAM News, October, 1999.
  • J. Guckenheimer and A. Khibnik, Torus maps from weak coupling of strong resonances, Contemporary Mathematics, Am. Math. Soc. Transl. (2), 200, 205-218, 2000.
  • J. Guckenheimer and A. Willms, Asymptotic analysis of subcritical Hopf-homoclinic bifurcation, Physica D, 139, 195-216, 2000.
  • J. Guckenheimer and B. Meloon, Computing Periodic Orbits and their Bifurcations with Automatic Differentiation, SIAM J. Sci Stat. Comp., 22, 951-985, 2000.
  • J. Guckenheimer, Periodic orbits of vector fields: Computational Challenges, International Conference on Differential Equations, Berlin 1999, B. Fiedler, K. Gr\"{o}ger and J. Spreckels, eds., World Scientific, 899-915, 2000.
  • J. Guckenheimer, K. Hoffman and W. Weckesser, Numerical computation of canards, Intl. J. Bifurcation and Chaos, 10, 2669-2687, 2000.
  • J. Guckenheimer, Computing periodic orbits, in Fluid mechanics and the environment: Dynamical Approaches, J. Lumley, ed., 107-120, 2001.
  • J. Guckenheimer and Y. Ilyashenko, The duck and the devil: canards on the staircase, Moscow mathematical Journal, 1, 27-48 2001.
  • J. Guckenheimer, review of Stephen Smale biography by Steve Batterson, Am. Math. Monthly, 108, 107-109, 2001.
  • J. Guckenheimer, K. Hoffman and W. Weckesser, Global analysis of periodic orbits in the forced van der Pol equation, in Global Analysis of Dynamical Systems, H. Broer, B. Krauskopf and G. Vegter, eds., IOP Press, 261-276, 2001.
  • J. Guckenheimer, Numerical analysis of dynamical systems, Handbook of Dynamical Systems, Elsevier, 2, 345-390, 2002.
  • J. Guckenheimer, Bifurcation and degenerate decomposition in multiple time scale dynamical systems, in Nonlinear Dynamics and Chaos: where do we go from here?  edited by John Hogan, Alan Champneys, Bernd Krauskopf,Mario di Bernardo, Eddie Wilson, Hinke Osinga, and Martin Homer, IOP Press, Bristol, pp. 1-21, 2002.
  • J. Guckenheimer and R. Oliva, Chaos in the Hodgkin-Huxley Model, SIAM J. Appl. Dyn. Systems, 1, 105-114, 2002.
  • J. Guckenheimer, K. Hoffman and W. Weckesser, The forced van der Pol equation I: the slow flow and its bifurcations, SIAM J. App. Dyn. Sys., 2, 1-35, 2002.
  • K. Bold, C. Edwards, J. Guckenheimer, S.  Guharay, K. Hoffman, Judith Hubbard, R. Oliva and W.  Weckesser, The forced van der Pol II: Canards in the Reduced System, SIAM J. App. Dyn. Sys.,2, 570-608, 2003.
  • J. Guckenheimer and Y. Xiang, Computing Singularities of Smooth Mappings, Moscow mathematical Journal, 3, 935-946, 2003.
  • Y. Zhang, R. Oliva, G. Gisselmann, H. Hatt, J. Guckenheimer and R. Harris-Warrick, Over-expression of an Ih channel gene modifies the firing activity of identified motor neurons in a small neural network, J. Neuroscience, 23: 9059-9067, 2003.
  • J. Guckenheimer, Bifurcations of Relaxation Oscillations, in Normal Forms, Bifurcations and Finiteness Problems in Differential Equations, Y. Ilyashenko and C. Rousseau, eds. Kluwer, 295-316, 2004.
  • S. Robertson, J. Guckenheimer, A. Masnick and L. Bacher, The dynamics of infant foraging, Developmental Science, 7, 194-200, 2004.
  • J. Guckenheimer and A. Vladimirsky, A fast method for approximation invariant manifolds, SIAM J. App. Dyn. Sys., 3, 232-260, 2004.
  • B. Krauskopf, H. Osinga, E. Doedel, M. Henderson, J. Guckenheimer, A. Vladimirsky, M. Dellnitz and O. Junge, A survey of methods for computing (un)stable  manifolds of vector fields, Int. J. Bifurcation and Chaos, 15, 763-792, 2005.
  • J. Guckenheimer and Radu Haiduc, Canards at folded nodes, Moscow Mathematical Journal, 25, 91-103, 2005.
  • M. Gruhn, J. Guckenheimer, B. Land, and R. M.Harris-Warrick, Dopamine modulation of two delayed rectifier potassium currents in a small neural network, J Neurophysiol, 94, 2888-2900, 2005.
  • Jason N. MacLean, Ying Zhang, Marie L. Goeritz, Richard Casey, Ricardo Oliva, John Guckenheimer, and Ronald M. Harris-Warrick, Activity-Independent Coregulation of IA and Ih in Rhythmically Active Neurons, J Neurophysiol, Nov 2005; 94: 3601 - 3617. 
  • J. Guckenheimer, K. Hoffman and W.  Weckesser, Bifurcations of relaxation oscillations near folded saddles, Int. J. Bif Chaos, 15, 3411-3421, 2005.
  • J. Guckenheimer, J. Tien and A. Willms, Bifurcations in the fast dynamics  of neurons: implications for bursting, in Bursting, The Genesis of Rhythm in the Nervous System,  Stephen Coombes and Paul C Bressloff eds., World Scientific, 89-122, 2005.
  • E. Phipps, R. Casey and J. Guckenheimer, Periodic orbits of hybrid systems and parameter estimation via AD, Lecture Notes in Computational Science and Engineering, 50, 211-224, 2006.
  • J. Guckenheimer, M. Wechselberger and Lai-Sang Young, Chaotic attractors of relaxation oscillators, Nonlinearity,  19, 701-720, 2006.
  • P. Holmes, R. Full, D. Koditschek and J. Guckenheimer, The dynamics of legged locomotion: models, analyses and challenges, SIAM Review, 48, 207-304, 2006.
  • S. Ellner and J. Guckenheimer, Dynamic Models in Biology, Princeton University Press, 2006.
  • Z. Ren, S.B. Pope, A. Vladimirsky and J.M. Guckenheimer, The ICE-PIC method for the dimension reduction of chemical kinetics, J. Chem. Phys. 124, 114111, 2006.
  • Z. Ren, S.B. Pope, A. Vladimirsky and J.M. Guckenheimer, Application of the ICE-PIC method for the dimension reduction of chemical kinetics coupled with transport,  Proceedings of the Combustion Institute, Volume 31, 473-481, 2007.
  • M. Venkadesan, J. Guckenheimer and F. Valero-Cuevas, Manipulating the edge of instability, J. Biomechanics, 40, 1653-1661, 2007.
  • J. Guckenheimer and D. LaMar, Periodic orbit continuation in multiple time scale systems. Numerical continuation methods for dynamical systems, 253--267, Underst. Complex Syst., Springer, Dordrecht, 2007.
  • J. Tien and J. Guckenheimer, Parameter estimation for bursting neural models, J. Comput. Neurosci. 24:358-373, 2008.
  • J. Guckenheimer, Return maps of folded nodes and folded saddle-nodes, Chaos, (9 pages), 18:015108, 2008.
  • R. Clewley, J. Guckenheimer and F. Valero-Cuevas, Estimating effective degrees of freedom in motor systems,  IEEE Trans. Biomed. Eng., 55, 430-442, 2008.
  • J. Guckenheimer, Singular Hopf bifurcation with two slow variables, SIAM J. App. Dyn. Sys., 7, 1355 2008.
  • S, Revzen and J. Guckenheimer, Estimating the phase of synchronized oscillators. Physical Review E (78), 051907, 2008.
  • J. Guckenheimer and C. Kuehn, Homoclinic orbits of the FitzHugh-Nagumo Equation: the singular-limit, DCDS-D, 2, 851-872, 2009.
  • J. Guckenheimer and C. Kuehn, Computing slow manifolds of saddle type, SIAM J. App. Dyn. Sys., 8, 854-879, 2009.
  • S. Carver, N. Cowan and J. Guckenheimer, Lateral stability of the spring-mass hopper suggests a two step control strategy for running, Chaos, 19:026106, 2009.
  • J. Guckenheimer and C. Kuehn, Homoclinic Orbits of the FitzHughNagumo Equation: Bifurcations in the Full System, SIAM J. App. Dyn. Sys., 9, 138-153, 2010.
  • L. Ristroph, A. Bergou, G. Ristroph, K. Coumes, G. Berman, J. Guckenheimer, Z. Wang, I. Cohen, Discovering the flight auto-stabilizer of fruit flies by inducing aerial stumbles, PNAS, , 2010 107 (11) 4820-4824.
  • X. Cao, J. Guckenheimer and L. Saloff-Coste, The backward behavior of the Ricci and cross-curvature flows on SL(2,R), Comm. in Analysis and Geometry, 17:4, 1-20, 2010.
  • A. Bergou, L. Ristroph, J. Guckenheimer, I. Cohen and Z. Wang, Fruit Flies Modulate Passive Wing Pitching to Generate In-Flight Turns, Phys. Rev. Lett. 104, 148101 (2010).
  • W. E. Sherwood and J. Guckenheimer, Dissecting the phase response of a model bursting neuron, SIAM J. App. Dyn. Sys., 2010.
  • W. E. Sherwood, R. Harris-Warrick and J. Guckenheimer, Synaptic Patterning of Left-Right Alternation in a Computational Model of the Rodent Hindlimb Central Pattern Generator, J. Comp. Neurosci., 2010.
  • J. Guckenheimer and C. Scheper, A Geometric Model for Mixed-Mode Oscillations in a Chemical System SIAM J. Appl. Dyn. Syst. 10, pp. 92-128, 2011.
  • J. Guckenheimer, A smooth multivariate interpolation algorithm, Panos Pardalos and Themistocles M. Rassias (eds.), Essays in Mathematics and its Applications. Dedicated to Stephen Smale, Springer, New York, 2011
  • S. Revzen and J. Guckenheimer. Finding the dimension of slow dynamics in a rhythmic system J. R. Soc. Interface. 9, 957-971, 2012
  • M. Desroches, J. Guckenheimer, B. Krauskopf, C. Kuehn, H. Osinga and M. Wechselberger, Mixed-Mode Oscillations with Multiple Time Scales, SIAM Review, 54:2, 211-288, 2012.
  • J. Guckenheimer and H. Osinga, The singular limit of a Hopf bifurcation, DCDS-A, 32:8, 2805-2823, 2012.
  • J. Guckenheimer, T. Johnson and P. Meerkamp, Rigorous enclosures of a slow manifold. SIAM J. Appl. Dyn. Syst. 11:3, 831-863, 2012.
  • J. Guckenheimer and P. Meerkamp, Unfoldings of singular Hopf bifurcations. SIAM J. Appl. Dyn. Syst. 11:4, 1325-1359, 2012.
  • L. Ristroph, A. Bergou, G. Berman, J. Guckenheimer, Z. Wang and I. Cohen, Dynamics, control and stabilization of turning flight in fruit flies, in Natural Locomotion in Fluids and on Surfaces, ed. S. Childress, A. Hosoi, W. Schultz and Z. Wang, Springer-Verlag, pp. 83-100, 2012.
  • L. Ristroph, G. Ristroph, S. Morozova, A. Bergou, S. Chang, J. Guckenheimer, Z. Jane Wang, and I. Cohen, Active and passive stabilization of body pitch in insect flight. J. R. SOC. Interface 10, 20130237 (May 2013)
  • J. Guckenheimer and C. Scheper, Multiple time scale analysis of a model Belousov-Zhabotinskii reaction. SIAM J. Appl. Dyn. Syst. 12:4, 1968-1996, 2013.
  • J. Guckenheimer, The birth of chaos, A. Johann et al. (eds.), Recent Trends in Dynamical Systems, Springer Proceedings in Mathematics & Statistics 35, 3-24, 2013.
  • S. Iams and J. Guckenheimer, Flight stability of mosquitos: a reduced model. SIAM J. Appl. Math. 74, 1535-1550, 2014.
  • J. Guckenheimer, From data to dynamical systems, Nonlinearity, 27, R41-R50, 2014.
  • H-M. Maus, S. Revzen, J. Guckenheimer, C. Ludwig, J. Reger, A. Seyfarth, Constructing predictive models of human running. J. R. Soc. Interface 12:20140899, 2015.
  • J. Guckenheimer and I. Lizarraga, Shilnikov homoclinic bifurcation of mixed-mode oscillations, SIAM J. Appl. Dyn. Syst., 14-2, pp. 764-786, 2015.
  • T. Beatus, J. Guckenheimer and I. Cohen, Controlling roll perturbations in fruit flies, J. R. Soc. Interface, 12 20150075; DOI: 10.1098/rsif.2015.0075. March 2015.
  • J. Guckenheimer, B. Krauskopf, H. Osinga and B. Sandstede, Invariant manifolds and global bifurcations, Chaos 25, 097604, http://dx.doi.org/10.1063/1.4915528, 2015.
  • Roberts, A., J. Guckenheimer, E. Widiasih, A. Timmermann, and C. Jones, 2016: Mixed mode oscillations of the El Niño-Southern Oscillation. J. Atmos. Sci. doi:10.1175/JAS-D-15-0191.1, 73-4,1755-1766, April 2016.
  • Analytic Research Foundations for the Next-Generation Electric Grid, The National Academies Press, 2016.
  • J. Guckenheimer, A. Timmermann, H. Dijkstra and A. Roberts (Un)predictability of strong El Niño events, Dynamics and Statistics of the Climate System, 2,1,dzx004, (https://doi.org/10.1093/climsys/dzx004), 2017.
  • J. Guckenheimer and A. Javeed, Locomotion: exploiting noise for state estimation, Biological Cybernetics, 113,93–104,2019.
  • J. Guckenheimer, Dense lines of curvature on convex surfaces, Proceedings of the American Mathematical Society, 2020.
  • Last Update: February 9, 2020