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.








    Mostly on dynamics, discontinuities, or singularities...

    (touch picture for abstract)

  1. Hidden Dynamics for Piecewise Smooth Maps
    Mike R Jeffrey and Paul Glendinning
    (2021)
    Nonlinearity
    34
    5
    3184-98
    preprint
    journal






  2. Bifurcations of hidden orbits in discontinuous maps
    Mike R Jeffrey and Viktor Avrutin
    (2021)
    Nonlinearity
    34
    9
    6140-72
    preprint
    journal






  3. Ageing of an oscillator due to frequency switching
    Carles Bonet, Mike R. Jeffrey, Pau Martin, Josep M. Olm
    (2021)
    Communications in Nonlinear Science and Numerical Simulation
    102
    105950
    1-26
    preprint
    journal






  4. Uncertainty in classical systems (with a local, non-stochastic, non-chaotic origin)
    Mike R. Jeffrey
    (2020)
    Journal of Physics A: Mathematical and Theoretical
    53
    115701
    1-15
    preprint
    journal (The journal version has an error in equation (7), for corrected version see here)






  5. The hidden unstable orbits of maps with gaps
    Mike R. Jeffrey and Simon Webber
    (2020)
    Proceedings of the Royal Society A
    476
    20190473
    1-19
    preprint
    journal






  6. The algebraic and differential building blocks of fundamental physical laws
    Mike R. Jeffrey
    (2020)
    preprint
    arxiv






  7. Complex geometry and fundamental physical law
    Mike R. Jeffrey
    (2019)
    preprint
    arxiv






  8. Two-fold singularities in nonsmooth dynamics -- higher dimensional analogues
    Simon Webber and Mike R. Jeffrey
    (2020)
    Chaos
    30
    9
    preprint
    journal






  9. Loss of determinacy at small scales, with application to multiple time-scale and nonsmooth dynamics
    Simon Webber and Mike R. Jeffrey
    (2020)
    IJBC
    in press
    preprint






  10. Modeling with nonsmooth dynamics
    Mike R. Jeffrey
    (2020)
    Frontiers in Applied Dynamical Systems (Springer)
    journal














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














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






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






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






  15. 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
    journal






  16. 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
    preprint
    journal






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






  18. 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
    preprint
    journal






  19. 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
    preprint
    journal






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






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






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






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






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






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






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






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






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






  29. 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
    preprint
    journal






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






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






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






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






  34. 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
    preprint
    arxiv
    journal






  35. 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
    preprint or low-tech draft(incomplete)
    or journal






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






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






  38. 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
    preprint
    journal






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






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






  41. 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
    preprint
    journal






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






  43. 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
    preprint






  44. 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
    preprint
    journal






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






  46. 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
    preprint
    journal






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






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






  49. 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
    preprint
    journal






  50. 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
    preprint
    journal






  51. 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
    preprint
    journal






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






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






  54. 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
    preprint
    journal






  55. 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
    preprint
    journal






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






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






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






  59. 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"
    preprint
    journal






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







    More from the Conical Diffraction years:

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






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

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

  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"
    preprint
    journal

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

  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
    preprint
    journal

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 July 2021 by MrJ.