Mike    Jeffrey

R.

Publications

Mike in Gaudi tower
Below you will find a complete list of my papers, along with links to preprints, glossy journal versions (alas these are not all freely downloadable), and other stuff. Help yourself. If you have questions or comments, my door is always open. Bring cake.
singularities
nonsmooth
friction
neuron spiking
bifurcation
sliding
impact
non-determinism

    Mostly on dynamics, discontinuities, or singularities...

    (touch picture for abstract)

  1. Uncertainty in classical systems (with a local, non-stochastic, non-chaotic origin)
    Mike R. Jeffrey
    (2019)
    submitted






  2. The algebra of differential geometry – complexity and curvature
    Mike R. Jeffrey
    (2019)






  3. The hidden unstable orbits of maps with gaps
    Mike R. Jeffrey and Simon Webber
    (2019)
    submitted






  4. Two-fold singularities in nonsmooth dynamics -- higher dimensional analogues
    Simon Webber and Mike R. Jeffrey
    (2019)
    in draft






  5. Small-scale loss of determinacy, with application to multiple time-scale and nonsmooth dynamics
    Simon Webber and Mike R. Jeffrey
    (2019)
    in draft






  6. Hidden Dynamics: The mathematics of switches, decisions, and other discontinuous behaviour
    Mike R. Jeffrey
    (2019)
    Springer monograph/textbook
    Order now from Springer or Amazon.
    And see its review in SIREV.














  7. Modeling with nonsmooth dynamics
    Mike R. Jeffrey
    (2019)
    Frontiers in Applied Dynamical Systems
    in review






  8. Pausing for arbitrarily long times in dynamical systems
    Simon Webber, Paul Glendinning, Mike R. Jeffrey
    (2019)
    Proc. R. Soc. A
    475
    20180574
    1-19






  9. Micro-slip as a loss of determinacy in dry friction oscillators
    Simon Webber, Mike R. Jeffrey
    (2019)
    IJBC
    29
    6
    1930015






  10. Jitter in dynamical systems with intersecting discontinuity surfaces
    Mike R. Jeffrey, Georgios Kafanas, David J. W. Simpson
    (2018)
    IJBC
    28
    06
    1-22






  11. On the Dulac's problem for piecewise analytic vector fields
    K. da S. Andrade, M. R. Jeffrey, R. M. Martins, M. A. Teixeira
    (2019)
    Journal of Differential Equations
    266
    4
    2259-73






  12. A unified approach to explain contrary effects of hysteresis and smoothing in nonsmooth systems
    Carles Bonet, Tere M. Seara, Enric Fossas, Mike R. Jeffrey
    (2017)
    Communications in Nonlinear Science and Numerical Simulation
    50
    142-168






  13. An Introduction to Piecewise Smooth Dynamics
    Paul A. Glendinning and Mike R. Jeffrey
    (2017)
    Advanced Courses in Mathematics - CRM Barcelona (Birkhauser)






  14. Regularization by External Variables
    E. Bossolini, R. Edwards, P. A. Glendinning, M. R. Jeffrey, S. Webber
    (2017)
    Extended Abstracts Spring 2016, Trends in Mathematics
    8
    19-24






  15. Integral Curves of a Vector Field with a Fractal Discontinuity
    Jonathan Hahn and Mike R. Jeffrey
    (2017)
    Extended Abstracts Spring 2016, Trends in Mathematics
    8
    95-99






  16. Why Nonsmooth?
    Mike R. Jeffrey
    (2017)
    Extended Abstracts Spring 2016, Trends in Mathematics
    8
    101-105






  17. An Update on that Singularity
    Mike R. Jeffrey
    (2017)
    Extended Abstracts Spring 2016, Trends in Mathematics
    8
    107-122






  18. Homoclinic boundary-saddle bifurcations in nonsmooth vector fields
    K. da S. Andrade, M. R. Jeffrey, R. M. Martins, M. A. Teixeira
    (2017)
    submitted






  19. The ghosts of departed quantities in switches and transitions
    Mike R. Jeffrey
    (2017)
    SIAM Review
    60
    1
    116–136






  20. Hidden bifurcations and attractors in nonsmooth dynamical systems
    Mike R. Jeffrey
    (2016)
    IJBC
    26
    4
    1650068(1-18)






  21. Smoothing tautologies, hidden dynamics, and sigmoid asymptotics in piecewise smooth systems
    Mike R. Jeffrey
    (2016)
    Chaos
    25
    103125
    1-11






  22. Exit from sliding in piecewise-smooth flows: deterministic vs. determinacy-breaking
    Mike R. Jeffrey
    (2016)
    Chaos
    26
    033108:1-20






  23. Hidden degeneracies in piecewise smooth dynamical systems
    Mike R. Jeffrey
    (2016)
    IJBC
    26
    5
    1650087:1-18






  24. Fast phase randomisation via two-folds
    David J. W. Simpson and Mike R. Jeffrey
    (2016)
    Proc. R. Soc. A
    472
    20150782(1-19)






  25. Piecewise smooth dynamical systems theory: the case of the missing boundary equilibrium bifurcations
    S. J. Hogan, M. Homer, M. R. Jeffrey, R. Szalai)
    (2016)
    Journal of Nonlinear Science
    26
    5
    1161-73






  26. Hidden dynamics of dry friction oscillators
    Mike R. Jeffrey
    (2015)
    Proc. of ICoEV Ljubljana, 7-10 September 2015






  27. Regularization of hidden dynamics in piecewise smooth flows
    Douglas D. Novaes, Mike R. Jeffrey
    (2015)
    Journal of Differential Equations
    259
    4615-33






  28. On the mathematical basis of solid friction
    Mike R. Jeffrey
    (2015)
    Nonlinear Dynamics
    81
    4
    1699-1716






  29. Hidden dynamics in models of discontinuity and switching
    Mike R. Jeffrey
    (2014)
    Physica D
    273-274
    34-45
    preprint or letter version(unproofed)






  30. Non-Filippov dynamics arising from the smoothing of nonsmooth systems, and its robustness to noise
    Mike R. Jeffrey and David J. W. Simpson
    (2014)
    Nonlinear Dynamics
    76
    2
    1395-1410






  31. Discontinuity-induced bifurcation cascades in flows and maps with application to models of the yeast cell cycle
    Mike R. Jeffrey and Harry Dankowicz
    (2014)
    Physica D, 271, 32-47






  32. Non-deterministic dynamics of a mechanical system
    Mike R. Jeffrey and Robert Szalai
    (2014)
    Physical Review E
    90
    022914
    1-11






  33. Dynamics at a switching intersection: hierarchy, isonomy, and multiple-sliding
    Mike R. Jeffrey
    (2014)
    SIADS
    13
    3
    1082–1105






  34. Grazing-sliding bifurcations, border collision maps and the curse of dimensionality for nonsmooth bifurcation theory
    Paul Glendinning and Mike R. Jeffrey
    (2015)
    Nonlinearity
    28
    263-283






  35. Singularities that induce a breakdown of determinism in mechanics
    Mike R. Jeffrey
    (2013)
    Proc. 5th International Conference on Strucural Dynamics SEMC, Cape Town






  36. The two-fold singularity: leading order dynamics in n-dimensions
    Alessandro Colombo and Mike R. Jeffrey
    (2013)
    Physica D
    263
    1-10






  37. Mathematical analysis of a model for the growth of the bovine corpus luteum
    S. A. Prokopiou, H. M. Byrne, M. R. Jeffrey, R. S. Robinson, G. E. Mann, and M. R. Owen
    (2013)
    Journal of Mathematical Biology
    69
    6-7
    1515-1546






  38. Nonsmooth analogues of slow-fast dynamics – pinching at a folded node
    Mathieu Desroches and Mike R. Jeffrey
    (2012)
    in limbo






  39. On sliding periodic solutions for piecewise continuous systems defined on the 2-cylinder
    Douglas D. Novaes, Mike R. Jeffrey and Marco A. Teixeira
    (2012)
    submitted






  40. Structural stability of the two-fold singularity
    S. Fernandez Garcia, D. Angulo Garcia, G. Olivar Tost, M. di Bernardo, M. R. Jeffrey
    (2012)
    SIADS
    11
    4
    1215-1230






  41. Non-determinism in the limit of nonsmooth dynamics
    M. R. Jeffrey
    (2011)
    Physical Review Letters
    106
    254103(1-4)
    journal or titbits in:






  42. Non-deterministic chaos, and the two-fold singularity of piecewise smooth flows
    A. Colombo and M. R. Jeffrey
    (2011)
    SIAM Journal on Applied Dynamical Systems
    10
    423-451






  43. The geometry of generic sliding bifurcations
    M. R. Jeffrey, S. J. Hogan
    (2011)
    SIAM Review
    53
    3
    505-525






  44. Canards and curvature: nonsmooth approximation by pinching
    M. Desroches and M. R. Jeffrey
    (2011)
    Nonlinearity
    24
    1655-1682






  45. Canards and curvature: the smallness of epsilon in slow-fast dynamics
    M. Desroches and M. R. Jeffrey
    2011
    Proceedings of the Royal Society A
    467
    2132
    2404-2421






  46. Bifurcations of piecewise smooth flows: perspectives, methodologies and open problems
    A. Colombo, M. di Bernardo, S. J. Hogan, M. R. Jeffrey
    (2012)
    Physica D, Special Issue on Nonsmooth Dynamical Systems
    241
    22
    1845-1860






  47. Three discontinuity-induced bifurcations to destroy self-sustained oscillations in a superconducting resonator
    M. R. Jeffrey
    (2012)
    Physica D, Special Issue on Nonsmooth Dynamical Systems
    241
    22
    2077-2082






  48. On hybrid dynamical systems with sliding
    M. R. Jeffrey
    (2010)
    draft, unpublished






  49. Sliding bifurcations and non-determinism in systems with switching
    M. R. Jeffrey
    (2011)
    Proc. Of the 18th IFAC World Congress, IFAC-PapersOnLine






  50. Teixeira singularities in 3D switched feedback control systems
    A. Colombo, M. di Bernardo, E. Fossas, M. R. Jeffrey
    (2009)
    Systems & Control Letters
    59
    10
    615-622






  51. Catastrophic Sliding Bifrucations, & onset of oscillations in a superconducting resonator
    M. R. Jeffrey, A. R. Champneys, M. di Bernardo, S. W. Shaw
    (2010)
    Physical Review E
    81
    016213-22






  52. Two-folds in nonsmooth dynamical systems.
    M. R. Jeffrey
    (2009)
    IFAC Chaos09 proceedings, Queen Mary June 2009






  53. The two-fold singularity of discontinuous vector fields
    M. R. Jeffrey, A. Colombo
    (2009)
    SIAM J. Appl. Dyn. Syst.
    8
    624-640






  54. Peel or coat spheres by convolution, repeatedly
    M. Schmidt, M. R. Jeffrey
    (2007)
    Journal of Mathematical Physics
    48
    123507(1-12)






  55. Orbital and spin angular momentum in conical diffraction
    M. V. Berry, M. R. Jeffrey, M. Mansuripur
    (2005)
    J. Optics A
    7
    685-690, Also featured as a "Highlight of 2006"






  56. The electric field of synchrotron radiation
    J. H. Hannay, M. R. Jeffrey
    (2005)
    Proc. R. Soc. A
    461
    3599-3610







    More from the Conical Diffraction years:

  1. Conical Diffraction: Complexifying Hamilton's Diabolical Legacy
    Mike R. Jeffrey
    (2007)
    Ph.D. Thesis, University of Bristol
     






  2. The spun cusp complexified: complex ray focusing in chiral conical diffraction
    M. R. Jeffrey
    (2007)
    J. Optics A
    9
    634-641

  3. Conical diffraction in optically active crystals
    M. R. Jeffrey
    (2006)
    IOP Photon06 online conference proceedings
     

  4. Conical diffraction complexified: dichroism and the transition to double refraction
    M. V. Berry, M. R. Jeffrey
    (2006)
    J. Optics A
    8
    1043-1051

  5. Conical diffraction: observations and theory
    M. V. Berry, M. R. Jeffrey, J. G. Lunney
    (2006)
    Proc. R. Soc. A
    462
    1629-1642, Also featured in "Top 10 most cited of 2005-2006"

  6. Chiral conical diffraction
    M. V. Berry, M. R. Jeffrey
    (2006)
    J. Optics A
    8
    363-372

  7. Conical diffraction: Hamilton's diabolical point at the heart of crystal optics
    M. V. Berry, M. R. Jeffrey
    (2006)
    Progress in Optics
    50
    13-50

A sound induction enabling us to predict, bearing not only stress, but torture: of theory actually remanding back experiment to read her lesson anew; informing her of facts so strange, as to appear to her impossible, and showing her all the singularities she would observe in critical cases she never dreamed of trying.

Sir John Herschel on Hamilton’s discovery of Conical Refraction, 1841 (Graves 1882)

Updated October 2019 by MrJ.