Publications


Books:


  1. J. P. Keener, Principles of Applied Mathematics; Transformation and Approximation , 2nd edition, Perseus Books, 1999.
  2. J. P. Keener and J. Sneyd, Mathematical Physiology , Springer, 2008 (Second Edition)

Journal Publications:

(This research has been supported by grants from the National Science Foundation and the National Institutes of Health)

  1. C. E. Miles and J. P. Keener, Jump locations of jump-diffusion processes with state-dependent rates Journal of Physics A: Mathematical and Theoretical 50 (2017).
  2. Lewis OL, Keener JP, Fogelson AL, A physics-based model for maintenance of the pH gradient in the gastric mucus layer. Am J Physiol Gastrointest Liver Physiol 2017 Sep 7;():ajpgi.00221.2017
  3. Bannish BE, Chernysh IN, Keener JP, Fogelson AL, Weisel JW, Molecular and Physical Mechanisms of Fibrinolysis and Thrombolysis from Mathematical Modeling and Experiments. Sci Rep 2017 Aug 7;7(1):6914
  4. Lawley SD, Keener JP, Rebinding in biochemical reactions on membranes. Phys Biol 2017 Jul 28;14(5):056002
  5. T. T. Renault, A. O. Abraham, T. Bergmiller , G. Paradis, S. Rainville, E. Charpentier, C. C. Guet, Y. Tu, K. Namba, J. P. Keener, T. Minamino , and M. Erhardt, Bacterial flagella grow through an injection-diffusion mechanism", eLife 2017;6:e23136 DOI: 10.7554/eLife.23136
  6. R. Magi and J. P. Keener, Modelling A Biological Membrane as a Two Phase Viscous Fluid with Curvature Elasticity, SIAM J. Appl. Math. 77,(1),128-153 (2017).
  7. S. Lawley and J. P. Keener, Including rebinding reactions in well-mixed models of distributive biochemical reactions, Biophysical J. 111, 10:2317-2326(2016).

  8. R. Veeraraghavan, J. Lin, J. P. Keener, R. Gourdie,S. Poelzing, Potassium Channels in the Cx43 Gap Junction Perinexus Modulate Ephaptic Coupling: An Experimental and Modeling Study, Pflugers Archiv - European Journal of Physiology, 2016 Oct;468(10):1651-61.
  9. V. Camacho, A. L. Fogelson, and J. P. Keener, Eulerian-Lagrangian treatment of non-dilute two-phase gels, SIAM J. Appl. Math. 76, pp. 341-367 (2016).
  10. S. D. Lawley and J. P. Keener, A New Derivation of Robin Boundary Conditions through Homogenization of a Stochastically Switching Boundary, SIAM J. Appl. Dyn. Sys. 14, pp. 1845-1867(2015).
  11. A. L. Fogelson and J. P. Keener, A Framework for Exploring the Post-gelation Behavior of Ziff and Stell's Polymerization Models SIAM Journal on Applied Mathematics, 75-3, pp. 1346-1368, (2015).
  12. Shtylla B, Keener JP, Mathematical modeling of bacterial track-altering motors: Track cleaving through burnt-bridge ratchets, Phys Rev E Stat Nonlin Soft Matter Phys 2015 Apr;91(4):042711
  13. S. George, K. J. Sciuto, J. Lin Ph.D, M. Salama Ph.D, J. P. Keener Ph.D, R. Gourdie Ph.D, S. Poelzing Ph.D, Extracellular sodium and potassium levels modulate cardiac conduction in mice heterozygous null for the Connexin43 gene. Pflugers Arch. 2015 Nov;467(11):2287-97. doi: 10.1007/s00424-015-1698-0. Epub 2015 Mar 14.
  14. S. George, K. J. Sciuto, J. Lin Ph.D, M. Salama Ph.D, J. P. Keener Ph.D, R. Gourdie Ph.D, S. Poelzing Ph.D, Effects of Extracellular Sodium and Potassium on Cardiac Conduction in Mice with Reduced Gap Junctional Coupling, Pflugers Archiv - European J. Physiology (2015) Oct;467(10):2093-105. doi: 10.1007/s00424-014-1675-z. Epub 2015 Jan 13.
  15. R. Veeraraghavan, J. Lin, J. P. Keener, R. Gourdie and S. Poelzing, Sodium Channels in the Cx43 Gap Junction Perinexus May Constitute a Cardiac Ephapse: An Experimental and Modeling Study, Pflugers Archiv - European Journal of Physiology. (2015).
  16. Miguel A. Dumett and J. P. Keener, The Pyrite Iron Cycle Catalyzed by \textit{Acidithiobacillus Ferroxidans}, J Math. Biol. 69, 449-67 (2014).
  17. Joyce Lin and J. P. Keener, Microdomain effects in transverse cardiac propagation, Biophys. J., 106,925-931 (2014).
  18. J. P. Keener and B. Shtylla, A mathematical model of force generation by flexible kinetochore-microtubule attachments, Biophysical J. 106, Pages 999--1007 (2014).
  19. B. E. Bannish, J. P. Keener, M. Woodbury, J. Weisel and A. L. Fogelson, Modelling Fibrinolysis: 1-D Continuum Models, MMB 31, 45-64 (2014).
  20. B. E. Bannish, J. P. Keener, and A. L. Fogelson, Modelling Fibrinolysis: A 3-Dimensional Stochastic Multiscale Model, MMB 31, 17-44 (2014).
  21. Hunter GA, Keener JP, Mechanisms underlying the additive and redundant Qrr phenotypes in Vibrio harveyi and Vibrio cholerae. J Theor Biol 2014 Jan 7;340:38-49

  22. Mageswaran SK, Dixon MG, Curtiss M, Keener JP, Babst M, Binding to Any ESCRT Can Mediate Ubiquitin-Independent Cargo Sorting. Traffic 15(2):212-29 (2014).

  23. Hunter GA, Vasquez FG, Keener JP, A mathematical model and quantitative comparison of the small RNA circuit in the Vibrio harveyi and Vibrio cholerae quorum sensing systems. Phys Biol 2013 Aug;10(4):046007

  24. Lin J, Keener JP, Ephaptic coupling in cardiac myocytes. IEEE Trans Biomed Eng 2013 Feb;60(2):576-82

  25. Sircar S, Keener JP, Fogelson AL, The effect of divalent vs. monovalent ions on the swelling of mucin-like polyelectrolyte gels: governing equations and equilibrium analysis. J Chem Phys 2013 Jan 7;138(1):014901

  26. A. Friedman, B. Hu and J. P. Keener, The diffusion approximation for linear non-autonomous reaction-hyperbolic equations, SIAM J. Math. Analysis 45(4): 2285-2298 (2013).
  27. Jian Du, Robert Guy, Aaron Fogelson, Grady Wright, and J. P. Keener, ``An interface-capturing regularization method for solving the equations for two-fluid mixtures", Communications in Computational Physics 14, 1322-1346 (2013).
  28. J. M. Newby, P. C. Bressloff, and J. P. Keener, Breakdown of fast-slow analysis in an excitable system with channel noise, Phys. Rev. Lett. 111, 128101 (2013)
  29. S. Sircar, J. P. Keener, and A. L. Fogelson, The Effect of Divalent vs. Monovalent ions on the Swelling of Mucin-like Polyelectrolyte Gels, J. Chem. Phys. Jan 7;138(1):014901(2013) .
  30. Rengasayee Veeraraghavan, Joyce Lin, James P Keener, Steven Poelzing, A Novel Role for Ephaptic Coupling in Cardiac Conduction: An Experimental and Modeling Study Biophysical Journal 102, 35a-36a (2012).
  31. B. Shtylla and J. P. Keener, A mathematical model of ParA filament-mediated chromosome movement in bacteria, J Theor Biol. 307:82-95 (2012).
  32. P. Childs and J. P. Keener, Slow Manifold Reduction of a Stochastic Chemical Reaction: Exploring Keizer's Paradox, Discrete Continuous Dynamical Systems-B, 17:1775-1794 (2012).
  33. Shu Dai and J. P . Keener, Using Noise to Determine Cardiac Restitution with Memory, Phys. Rev. E 85, 061902 (2012).
  34. Du J, Keener JP, Guy RD, Fogelson AL, Low-Reynolds-number swimming in viscous two-phase fluids. Phys Rev E Stat Nonlin Soft Matter Phys 2012 Mar;85(3 Pt 2):036304

  35. Keener JP, Newby JM, Perturbation analysis of spontaneous action potential initiation by stochastic ion channels. Phys Rev E Stat Nonlin Soft Matter Phys 2011 Jul;84(1 Pt 1):011918

  36. Keener JP, Sircar S, Fogelson AL, Influence of the standard free energy on swelling kinetics of gels. Phys Rev E Stat Nonlin Soft Matter Phys 2011 Apr;83(4 Pt 1):041802

  37. Erhardt M, Singer HM, Wee DH, Keener JP, Hughes KT, An infrequent molecular ruler controls flagellar hook length in Salmonella enterica. EMBO J 2011 Jun 7;30(14):2948-61

  38. J. Newby and J. P. Keener. An asymptotic analysis of the spatially-inhomogeneous velocity-jump process, SIAM Multiscale Modeling and Simulation, 9:735-765 (2011).
  39. J. P. Keener, S. Sircar and A. L. Fogelson, Kinetics of swelling gels, SIAM J. Appl. Math. 71, pp. 854-875 (2011).
  40. B. Shtylla and J. P. Keener, A mathematical model for force generation at the kinetochore-microtubule interface, SIAM J. Appl. Math. 71, pp. 1821-1848 (2011).
  41. Lin J, Keener JP, Modeling electrical activity of myocardial cells incorporating the effects of ephaptic coupling. Proc Natl Acad Sci U S A 2010 Dec 7;107(49):20935-40

  42. Tania N, Keener JP, Calsequestrin mediates changes in spontaneous calcium release profiles. J Theor Biol 2010 Aug 7;265(3):359-76

  43. A. L. Fogelson and J. P. Keener "Toward an understanding of fibrin branching structure" Physical Review E, Vol.81, No.5, 051922 (2010).
  44. Berton Earnshaw and J. P. Keener, "Invariant Manifolds of Binomial-Like Nonautonomous Master Equations," SIADS, Volume 9, Issue 2, pp. 568-588 (2010).
  45. Berton Earnshaw and J. P. Keener, Global asymptotic stability of solutions of nonautonomous master equations, SIAM J. Appl. Dyn. Syst., 9, pp. 220-237 (2010).
  46. N.-P. Nguyen, C. Myers, H. Kuwahara, C. Winstead, and J. Keener, Design and Analysis of a Robust Genetic Muller C-element, J. Theor. Biol. ,264, Issue 2, 21 May 2010, Pages 174-187.
  47. Blerta Shtylla and J. P. Keener, A mechano-molecular model for the movement of chromosomes during mitosis driven by a minimal kinetochore bicyclic cascade J. Theor. Biol. Volume 263, Issue 4, 21 April 2010, Pages 455-470
  48. Keener, JP, Exact reductions of Markovian dynamics for ion channels with a single permissive state. J Math Biol 2009
  49. J. P. Keener, A molecular ruler mechanism for length control of extended protein structures in bacteria. J. Theor. Biol.(2009),doi:10.1016/j.jtbi.2009.12.015
  50. J. P. Keener, Invariant Manifolds Reductions for Markovian Ion Channel Dynamics, J. Math. Biol.: 58, 447 (2009)
  51. E. D. Copene and J. P. Keener, Ephaptic Coupling of Cardiac Cells Through the Junctional Electrical Potential, J. Math Biology, Volume 57, Number 2, 265-284, (2008), DOI: 10.1007/s00285-008-0157-3.
  52. Y.-S. Lee and J. P. Keener, A calcium-induced calcium release mechanism mediated by calsequestrin J. Theoretical Biology. 253, 4, Pages 668679(2008)

  53. N.-P. D. Nguyen, H. Kuwahara, C. J. Myers, and J. P. Keener, The Design of a Genetic Muller C-Element, In The 13th IEEE International Symposium on Asynchronous Circuits and Systems, 2007 (ASYNC 07) Best Paper Award.
  54. R. D. Guy, A. L. Fogelson, and J. P. Keener, Fibrin gel formation in a shear flow Math. Med. Biol.(2007)

  55. Keener, J. How Salmonella typhimurium measures the length of flagellar filaments. Bull. Math. Biol. 68(7):1761-78(2006)

  56. Keener, J Stochastic calcium oscillations. Math Med Biol 23: 1-25(2006)

  57. J. M. Zobitz, J. P. Keener, H. Schnyder and D. R. Bowling, Sensitivity analysis and quantification of uncertainty for isotopic mixing relationships in carbon cycle research, Agricultural and Forest Meteorology, 136, 56-75 (2006).
  58. Keener J , A model for length control of flagellar hooks of Salmonella typhimurium. J. Theor. Biol. 2005 May 21;234(2):263-75

  59. B. E. Peercy and J. P. Keener, Coupled cell model of border zone arrhythmias, SIAM J. Appl. Dyn. Sys,4, 679-710 (2005)
  60. N. Cogan and J. P. Keener, Channel Formation in Gels, SIAM J. Appl. Math. , 65, 1839-1854 (2005).
  61. M. Dumett and J. P. Keener, An immersed interface method for Anisotropic Elliptic Problems on Irregular Domains in 2D, Num. Methods Partial Differetnial Eqs. 21:397-420, 2005.
  62. Keener J , The topology of defibrillation. J Theor Biol 2004 Oct 21;230(4):459-73

  63. N. Cogan and J. P. Keener, The role of the biofilm matrix in structural development, Mathematical Medicine and Biology, 21, 147-166 (2004).
  64. J. P. Keener, Model for the onset of fibrillation following coronary artery occlusion. J Cardiovasc Electrophysiol 2003 Nov;14(11):1225-32

  65. J. P. Keener and E. Cytrynbaum , The effect of spatial scale of resistive inhomogeneity on defibrillation of cardiac tissue. J Theor Biol 2003 Jul 21;223(2):233-48

  66. Yi CS, Fogelson AL, Keener JP, Peskin C , A mathematical study of volume shifts and ionic concentration changes during ischemia and hypoxia. J Theor Biol 2003 Jan 7;220(1):83-106

  67. M. Dumett and J. P. Keener, A Numerical Method for Solving Anisotropic Elliptic Boundary Value Problems in 3D, SIAM J. Sci. Comp. 25, 348-367 (2003).

  68. E. Cytrynbaum and J. P. Keener, Stability conditions for the Traveling Pulse - Modifying the restitution hypothesis, Chaos, 12, 788-799 (2002).
  69. Spitzer KW, Skolnick RL, Peercy BE, Keener JP, Vaughan-Jones R , Facilitation of intracellular H(+) ion mobility by CO(2)/HCO(3)(-) in rabbit ventricular myocytes is regulated by carbonic anhydrase. J Physiol 2002 May 15;541(Pt 1):159-67

  70. R. D. Vaughan-Jones, B. E. Peercy, J. P. Keener, and K. W. Spitzer, Intrinsic H+ ion mobility in the mammalian ventricular myocyte, J. Physiology,541.1, 139-158 (2002).
  71. J. P. Keener, Arrhythmias by Dimension, in An Introduction to Mathematical Modeling in Physiology, Cell Biology, and Immunology, Proc. Symp. Applied Math., AMS, 59, ed. J. Sneyd, 2002.
  72. A. Fogelson and J. P. Keener, Immersed interface methods for Neumann and related problems in two and three dimensions, Siam J. for Scientific Computing, 22, 1630-1654 (2001).Abstract
  73. J. D. Dockery and J. P. Keener, A Mathematical model for quorum sensing in Pseudomonas Aeruginosa, Bull. Math. Biol. 63, 95-116 (2001). Abstract

  74. Keener J , Diffusion induced oscillatory insulin secretion. Bull Math Biol 2001 Jul;63(4):625-41
  75. J. P. Keener, Propagation of Waves in an Excitable Medium with Discrete Release Sites, SIAM J. Appl. Math. 61, 317-334 (2000).Abstract

  76. A. V. Panfilov, S. C. M\"{u}ller, V. S. Zykov and J. P. Keener, Defibrillation of cardiac tissue by multiple subthreshold shocks, Phys. Rev. E, 61, 4644-4647 (2000).
  77. T. J. Lewis and J. P. Keener, Wave-Blocking in excitable media due to regions of depressed excitability, SIAM J. Appl. Math., 61, 293-316 (2000).
  78. A. V. Panfilov, S. C. Muller, V. S. Zykov and J. P. Keener, Defibrillation of cardiac tissue by multiple subthreshold shocks, Phys. Rev. E, 61, 4644-4647 (2000).
  79. J. P. Keener, Homogenization and propagation in the bistable equation, Physica D 136, 1-17 (2000).Abstract
  80. Keener JP, Lewis T , The biphasic mystery: why a biphasic shock is more effective than a monophasic shock for defibrillation. J Theor Biol 1999 Sep 7;200(1):1-17Abstract (Nice pictures)

  81. Keener JP, Bogar , A numerical method for the solution of the bidomain equations in cardiac tissue. Chaos 1998 Mar;8(1):234-241

  82. Keener J , The effect of gap junctional distribution on defibrillation. Chaos 1998 Mar;8(1):175-187

  83. J. P. Keener and A. V. Panfilov, The effects of geometry and fiber orientation on propagation and extracellular potentials in myocardium, in Computational Biology of the Heart, eds. A. V. Holden and A. V. Panfilov, Wiley, 1997.
    Abstract
  84. Keener JP, Panfilov A , A biophysical model for defibrillation of cardiac tissue. Biophys J 1996 Sep;71(3):1335-45Abstract

  85. Keener J , Direct activation and defibrillation of cardiac tissue. J Theor Biol 1996 Feb 7;178(3):313-24

    Abstract
  86. M. Courtemanche, J. P. Keener, and L. Glass, A delay equation representation of pulse circulation on a ring in excitable media, SIAM J. Appl. Math., 56, 119-142, (1996).
  87. A.V. Panfilov and J. P. Keener, Reentry in 3-Dimensional FitzHugh-Nagumo medium with rotational anisotropy, Physica D 84, 545-552 (1995).

  88. A. V. Panfilov and J. P. Keener, Dynamics of dissipative structures in excitable media, SIAM J. Appl. Math. 55, 205-219 (1995).

  89. A. V. Panfilov and J. P. Keener, Re-entry in an anatomical model of the heart, Chaos, Solitons, and Fractals, 5, 681-689 (1995).Abstract
  90. J. P. Keener and A. V. Panfilov, Three dimensional propagation in the heart: The effects of geometry and fiber orientation on propagation in myocardium, in Cardiac Electrophysiology, eds. D. P. Zipes and J. Jalife, W. B. Saunders Company, 335-348, 1995.
    Abstract
  91. J. P. Keener, Wave propagation in myocardium, in Theory of Heart, ed. L. Glass, P. Hunter, A. McCullock, Springer-Verlag, pp. 405-436.
  92. J. J. Tyson and J. P. Keener, A theory of rotating scroll waves in excitable media, in Chemical Waves (R. Kapral and K. Showalter, eds.) 93-118, Kluwer, Dordrecht, 1994.

  93. K. Agladze, J. P. Keener, S. C. Müller, and A. V. Panfilov, Rotating spiral waves created by geometry, Science 264, 1746-1748 (1994). Abstract

  94. J. P. Keener, Symmetric Spirals in Media with Relaxation Kinetics and Two Diffusing species, Physica D 70, 61-73 (1994).

  95. A. V. Panfilov and J. P. Keener, Effects of high frequency stimulation on cardiac tissue with an inexcitable obstacle, J. Theor. Biol. 163, 439-448 (1993).

  96. A. V. Panfilov and J.P. Keener, Modeling reentry in a finite element model of the heart, J.Physiol. 467, 152P (1993).

  97. Panfilov AV, Keener J , Generation of reentry in anisotropic myocardium. J Cardiovasc Electrophysiol 1993 Aug;4(4):412-21

  98. M. Courtemanche, L. Glass and J. P. Keener, Instabilities of a propagating pulse in a ring of excitable media, Phys. Rev. Letts., 70, 2182-2185 (1993).
  99. A. V. Panfilov and J. P. Keener, Twisted scroll waves in heterogeneous excitable media, Int. J. Bifurcation and Chaos, 3, 445-450 (1993).

  100. J. P. Keener, The Perron-Frobenius Theorem and the ranking of football teams, SIAM Rev., 35, 80-93, (1993).

  101. J. P. Keener, Uses and Abuses of numerical analysis in cardiology, in The Dynamics of Numerics and the Numerics of Dynamics, ed. D.S. Broomhead and A. Iserles, Claredon Press, Oxford, 195-213, 1992.

  102. J. P. Keener, The core of the spiral, SIAM J. Appl. Math., 52, 1372-1390 (1992).

  103. J. P. Keener and J. J. Tyson, The Dynamics of Scroll Waves in Excitable Media, SIAM Rev., 34, 1-39 (1992).

  104. J. P. Keener and J. J. Tyson, The dynamics of helical scroll waves in excitable media, Physica D, 53, 151-161 (1991).

  105. Keener J , An eikonal-curvature equation for action potential propagation in myocardium. J Math Biol 1991;29(7):629-51

  106. Keener J , The effects of discrete gap junction coupling on propagation in myocardium. J Theor Biol 1991 Jan 7;148(1):49-82

  107. Keener J , The effects of gap junctions on propagation in myocardium: a modified cable theory. in Mathematical Approaches to Cardiac Arrhythmias, Ann N Y Acad Sci 1990;591():257-277

  108. J. P. Keener and J. J. Tyson, Helical and circular scroll wave filaments, Physica D, 44, 191- 202 (1990).

  109. J. P. Keener, Wave propagation in myocardium, in Theory of Heart, ed. L. Glass, P. Hunter, A. McCullock, Springer-Verlag, pp. 405-436.

  110. J. P. Keener, Knotted vortex filaments in an ideal fluid, J. Fluid Mech. 211, 629-651 (1990).

  111. J. P. Keener, A Mathematical Model for the Initiation of Ventricular Tachycardia in Myocardium, in Cell-to-Cell Signalling: From Experiments to Theoretical Models, 589-608, ed. A. Goldbeter, Academic Press, 1989.
  112. J. P. Keener and F. M. Phelps IV, Consequences of the Cellular, Anisotropic Structure of Myocardium, in Some Mathematical Questions in Biology, The Dynamics of Excitable Media, Lectures on Mathematics in the Life Sciences, Volume 21, ed H. Othmer, AMS, Providence, 1989.

  113. J. P. Keener, Knotted Scroll Wave Filaments in Excitable Media, Physica D 34, 378-390, (1989).

  114. J. D. Dockery and J. P. Keener, Diffusive Effects on Dispersion in Excitable Media, SIAM J. Appl. Math., 49, 539-566, (1989).

  115. J. J. Tyson and J. P. Keener, Singular Perturbation Theory of Spiral Waves in Excitable Media, Physica D 32, 327-361 (1989).

  116. J. P. Keener, Frequency Dependent Decoupling of Parallel Excitable Fibers, SIAM J. Appl. Math., 49, 210-230, (1989).
  117. Keener J , On the formation of circulating patterns of excitation in anisotropic excitable media. J Math Biol 1988;26(1):41-56
  118. J. P. Keener, A Mathematical Model for the Vulnerable Phase in Myocardium, Math. Biosci. 90, 3- 18, (1988).

  119. J. P. Keener, The Dynamics of Three Dimensional Scroll Waves in Excitable Media, Physica D 31, 269-276 (1988)

  120. J. D. Dockery, J. P. Keener, and J. J. Tyson, Dispersion in the Belousov-Zhabotinskii Reaction, Physica D 30, 177-191 (1988).

  121. J. P. Keener, On the Formation of Circulating Patterns of Excitation in Anisotropic Excitable Media, J. Math. Biology, 26, 41-57 (1988).

  122. J. P. Keener and J. J. Tyson, The Motion of Untwisted Untorted Scroll Waves in Belousov-Zhabotinsky Reagent, Science 239, 1284-1286 (1988).

  123. J. J. Tyson and J. P. Keener, Spiral Waves in a Model of Myocardium, Physica D 29, 215- 222 (1987).

  124. J. P. Keener, Causes of Propagation Failure in Excitable Media, Temporal Disorder in Human Oscillatory Systems, eds. L. Rensing, U. an der Heiden, M. C. Mackey, Springer Verlag, Berlin, 1987.

  125. J. P. Keener, Propagation and its Failure in Discrete Systems of Coupled Excitable Cells, SIAM J. Appl. Math. 47, 556-572 (1987).

  126. W. C. Troy, E. A. Overman, G. B. Ermentrout and J. P. Keener, Uniqueness of a flow of a second order fluid past a stretching sheet, Quart. J. Appl. Math. 44, 753-755 (1987).

  127. J. P. Keener, Propagation and its Failure in the Discrete Nagumo Equation, in Ordinary and Partial Differential Equations, eds. B. D. Sleeman and R. J. Jarvis, Pitman Research Notes in Mathematics Series, 157, 95-112, Longman, New York, 1987.

  128. J. P. Keener, A Geometrical Theory for Spiral Waves in Excitable Media, SIAM J. Appl. Math., 46, 1039-1056 (1986).

  129. J. P. Keener, A Sarkovskii Ordering for Stable Periodic Orbits of Maps of the Interval, SIAM J. Num. Anal., 23, 976-985 (1986).

  130. J. P. Keener and J. J. Tyson, Spiral Waves in the Belousov-Zhabotinskii Reaction, Physica D, 21, 307-324 (1986).

  131. J. P. Keener, Spiral Waves in Excitable Media, Lecture Notes in Biomathematics,66, Springer, 115-127, (1986).

  132. F. T. Krogh, J. P. Keener, and W. H. Enright, Reducing the Number of Variational Equations in the Implementation of Multiple Shooting, Progress in Scientific Computing, Vol. 5, Birkhauser Boston, (1985).

  133. J. P. Keener, Oscillatory Coexistence in a Food Chain Model with Competing Predators, J. Math. Biol. 22, 123-136 (1985).

  134. J. P. Keener and L. Glass, Global bifurcations of a periodically forced nonlinear oscillator, J. Math. Biol., 21, 123-136 (1984).

  135. J. P. Keener, Dynamic Patterns in Excitable Media, Lecture Notes in Biomathematics, 55, 157-169, Springer Verlag, Berlin, 1984.

  136. K. Beck, J. P. Keener, and P. Ricciardi, The Effect of Epidemics on Genetic Evolution, J. Math. Biol., 19, 63-77 (1984).

  137. J. P. Keener, Analogue Circuitry for the van der Pol and Fitzhugh Nagumo Equations, IEEE Trans. on Systems, Man, Cybernetics, 13, 5, 1010-1014 (1983).

  138. J. P. Keener and J. Rinzel, Hopf Bifurcation to Repetitive Activity in Nerve, SIAM J. Appl. Math. 43, 907-922 (1983).

  139. J. P. Keener, Oscillatory Coexistence in the Chemostat: A Codimension Two Unfolding, SIAM J. Appl. Math., 43, 5, 1005-1018 (1983).

  140. J. P. Keener, Diffusion Induced Chaos, Contemporary Mathematics,17, 293-391 (1983).

  141. K. Beck, J. P. Keener and P. Ricciardi, Influence of Infectious Disease on the Growth of a Population with Three Genotypes, Lecture Notes in Biomathematics,52, Springer, 1983.

  142. J. P. Keener, Chaotic Behavior in Slowly Varying Systems of Nonlinear Differential Equations, Stud. Appl. Math., 67, 25-44 (1983).

  143. F. C. Hoppensteadt and J. P. Keener, Phase Locking of Biological Clocks, J. Math. Biol., 15, 339-349(1982).

  144. J. P. Keener, Infinite Period Bifurcation in Simple Chemical Reactors, in Modelling of Chemical Reaction Systems, Chemical Physics 18, Springer ed., K. H. Ebert, P. Dueflhard, and W. Jager, 1981.

  145. J. P. Keener, On Cardiac Arrhythmias: AV Conduction Block, J. Math. Biol., 12, 215-225 (1981).

  146. J. P. Keener, Infinite Period Bifurcation and Global Bifurcation Branches, SIAM J. Appl. Math., 41, 127-144 (1981).

  147. J. P. Keener, F. C. Hoppensteadt, J. Rinzel, Integrate and Fire Models of Nerve Membrane Response to Oscillatory Input , SIAM J. Appl. Math., 41, 503-517 (1981).

  148. J. P. Keener, Chaotic Cardiac Dynamics, Mathematical Aspects of Physiology, Lectures in Applied Mathematics, 19, 299-325 (1981).

  149. J. P. Keener, Waves in Excitable Media, SIAM J. Appl. Math., 39, 3, 528-548 (1980).

  150. J. P. Keener, Chaotic Behavior in Piecewise Continuous Difference Equations, AMS Transactions, 261, 589-604 (1980).

  151. J. P. Keener, Secondary Bifurcation and Multiple Eigenvalues, SIAM J. Appl. Math., 37, 330- 349 (1979).

  152. J. P. Keener, Long Range Predation in Pattern Formation, Rocky Mtn. J. Math., 9, 1, 99-114 (1979).

  153. J. P. Keener, Activators and Inhibitors in Pattern Formation, Stud. Appl. Math., 59, 1-23 (1978).

  154. J. P. Keener and D. W. McLaughlin, A Green's Function for a Linear Equation Associated with Solitons, J. Math. Phys., 16, 2008-2013 (1977).

  155. J. P. Keener and D. W. McLaughlin, Solitons under perturbation, Phys. Rev. A, Vol. 6, No. 2 777-790 (1977).

  156. J. P. Keener, On the validity of the two-timing method for long times, SIAM J. Math. Anal., Vol. 8, No. 6 (1977).

  157. J. P. Keener, Secondary Bifurcation in Nonlinear Diffusion-Reaction Equations, Stud. Appl. Math., 55,187-211 (1976).

  158. D. S. Cohen and J. P. Keener, Multiplicity and Stability of Oscillatory States in a Continuous Stirred Tank Reactor with Exothermic Consecutive Reactions A . B. C, Chem. Eng. Sci., Vol. 31, 115-122 (1976).

  159. J. P. Keener and D. S. Cohen, Nonlinear Oscillations in a Reactor with Two Temperature Coefficients, Nuclear Sci. Eng., Vol. 56, 354-359 (1975).

  160. D. S. Cohen and J. P. Keener, Oscillatory Processes in the Theory of Particulate Formation in Super-saturated Chemical Solutions, SIAM J. Appl. Math., Vol. 28, #2, 307-318 (1975).

  161. J. P. Keener, Perturbed Bifurcation Theory at Multiple Eigenvalues, Arch. Rat. Mech. Anal., Vol. 56, #4, 348-366 (1974).

  162. J. P. Keener, Imperfection Sensitivity of Buckling for Columns and Spherical Caps, Quart. Appl. Math., 173-188 (1974).

  163. J. P. Keener and H. B. Keller, Positive Solutions of Convex Nonlinear Eigenvalue Problems, J. Diff. Eqns., Vol. 16, #1, 103-125 (1973).

  164. A. D. Randolph, G. L. Beer, and J. P. Keener, Stability of the Class II Classified Product Crystallizer with Fines Removal, AIChE. Journal, Vol. 19, #6, 1140-1149 (1973).

  165. J. P. Keener and H. B. Keller, Perturbed Bifurcation Theory, Arch. Rat. Mech. Anal., Vol. 50, #3, 159-175 (1973).

  166. J. P. Keener and H. B. Keller, Perturbed Bifurcation and Buckling of Circular Plates, Conference on Ordinary and Partial Differential Equations, University of Dundee, Lecture Notes in Mathematics, #280, Springer, 286-293 (1972).



Jim Keener 2014-1-22