Preprints, papers and books
Paul Glendinning Shaking and whirling: dynamics of spiders and their webs.
Paul Glendinning and Sasha Glendinning Smooth conjugacy of difference equations derived from elliptic curves.
Paul A. Glendinning, David J.W. Simpson, Constructing robust chaos: invariant manifolds and expanding cones, arXiv:1906.11969
Gianne Derks, Paul A. Glendinning, Anne C. Skeldon, Creation of discontinuities in circle maps, arXiv:1903.06968
Publications: articles and books
-  Biga V, Hawley J, Soto, X, Johns E, Han D, Bennett H, Adamson A.D, Kursawe, J, Glendinning P, Manning C. and Papalopulu N.
A dynamic, spatially periodic, micro-pattern of HES5 underlies neurogenesis in the mouse spinal cord (2021), to appear Molecular Systems Biology.
-  P. Glendinning and M.R. Jeffrey (2021) Hidden dynamics for piecewise smooth maps, to appear, Nonlinearity.
-  Paul A. Glendinning and David J.W. Simpson (2021) A constructive approach to robust chaos using
invariant manifolds and expanding cones, Disc. Cont. Dynam. Syst. Series A, Discrete & Continuous Dynamical Systems - A (DCDS-A) 41(7) doi:10.3934/dcds.2020409.
-  RN Thompson, TD Hollingsworth, V Isham, D Arribas-Bel, B Ashby, and many others including P. Glendinning (2020) Key questions for modelling COVID-19 exit strategies, Proc. Roy. Soc. B 287
-  Paul A. Glendinning and David J.W. Simpson (2020) Robust Chaos and the Continuity of Attractors,
Trans. Math. & Its Appl. 4(1) doi.org/10.1093/imatrm/tnaa002.
-  Paul Glendinning (2020) Adaptive resonance and pumping a swing.
European Journal of Physics, 41 025006, doi.org/10.1088/1361-6404/ab6a63.
-  Paul Glendinning and Mike R. Jeffrey (2019) An Introduction to Piecewise Smooth Dynamics, Birkh\"auser.
-  S. Webber, P. Glendinning and M.R. Jeffrey (2019) Pausing for arbitrarily long times in dynamical systems
Proc. Roy. Soc. A 475, 2221, 20180574.
-  Paul Glendinning (2018) Shilnikov chaos, Filippov sliding and boundary equilibrium bifurcations
EJAM 29, 757--777.
-  Paul Glendinning (2018) Three haiku J. Humanistic Math. 8(1), 454.
-  Paul Glendinning (2017) Less Is More II: An Optimistic View of Piecewise Smooth Bifurcation Theory, pp. 77-81 in Extended Abstracts Spring 2016 Nonsmooth Dynamics (Research Perspectives CRM Barcelona) eds. A. Colombo, M.R. Jeffrey, J.T. Lazaro and J.M. Olm, Springer.
-  Paul Glendinning (2017) Less Is More I: A Pessimistic View of Piecewise Smooth Bifurcation Theory, pp. 71-75 in Extended Abstracts Spring 2016 Nonsmooth Dynamics (Research Perspectives CRM Barcelona) eds. A. Colombo, M.R. Jeffrey, J.T. Lazaro and J.M. Olm, Springer.
-  Chris Budd, Paul Glendinning, Kaitlin Hill, and Rachel Kuske (2017) Characterizing Tipping in a Stochastic Reduced Stommel-Type Model in Higher-Dimensions, pp. 25-29 in Extended Abstracts Spring 2016 Nonsmooth Dynamics (Research Perspectives CRM Barcelona) eds. A. Colombo, M.R. Jeffrey, J.T. Lazaro and J.M. Olm, Springer.
-  E. Bossolini, R. Edwards, P. A. Glendinning, M. R. Jeffrey, S. Webber (2017) Regularization by External Variables, pp. 19-24 in Extended Abstracts Spring 2016 Nonsmooth Dynamics (Research Perspectives CRM Barcelona) eds. A. Colombo, M.R. Jeffrey, J.T. Lazaro and J.M. Olm, Springer.
-  Paul Glendinning (2017) Robust chaos revisited, European Physical Journal Special Topics, 226: 1721. doi:10.1140/epjst/e2017-70058-2
-  Paul Glendinning (2016)
Geometry of refractions and reflections through a biperiodic medium, SIAM J. Appl. Math., 76(4), 1219–1238
-  Paul Glendinning, Piotr Kowalczyk and Arne Nordmark (2016)
Multiple attractors in grazing-sliding bifurcations in an explicit example of Filippov type, IMA J Appl Math. doi: 10.1093/imamat/hxw014.
-  Paul Glendinning (2016)
Bifurcation from stable fixed point to two-dimensional attractor in the border collision normal form,
IMA J. Appl. Math. doi: 10.1093/imamat/hxw001
-  Paul Glendinning (2016) Classification of Boundary
Equilibrium Bifurcations of planar Filippov systems, Chaos 26, 013108; http://dx.doi.org/10.1063/1.4940017
-  Paul Glendinning (2015) Bifurcation from stable fixed point to $N$-dimensional attractor in the border collision normal form, Nonlinearity 28(10): 3457-3464.
-  N. J. Higham (Editor) Princeton Companion to Applied Mathematics, Princeton, 2015 (Associate Editor and Contributor).
-  P. Glendinning and N. Sidorov (2015) The doubling map with asymmetric holes, Ergod. Th.& Dynam. Syst. 35, 1208 - 1228
DOI:10.1017/etds.2013.98 [21 pages]
-  P Glendinning and M R Jeffrey (2015) Grazing-sliding bifurcations, border collision maps and the curse of dimensionality for piecewise smooth bifurcation theory, Nonlinearity 28 263-283 (doi:10.1088/0951-7715/28/1/263) -- very early draft on eprints.
-  Andrew Roberts and Paul Gendinning (2014) Canard-like phenomena in piecewise-smooth Van der Pol systems, Chaos 24, 02313; http://dx.doi.org/10.1063/1.4885502
-  P. Glendinning (2014) Invariant Measures for the n-Dimensional Border Collision Normal Form, IJBC 24 (12) 1450164 DOI: 10.1142/S0218127414501648
-  P.Glendinning (2014) Renormalization for the boundary of chaos in piecewise monotonic maps with a single discontinuity, Nonlinearity 27 R143-R162 (doi:10.1088/0951-7715/27/12/R143)
-  V. Botella-Soler and P.Glendinning (2014) Hierarchy and polysynchrony in an adaptive network. Phys. Rev. E 89 062809.
-  Mora, Karin; Budd, Chris; Glendinning, Paul; Keogh, Patrick (2014) Non-smooth Hopf-type bifurcations arising impact–friction contact events in rotating machinery. Proc. Roy. Soc. A, 470: 20140490.
-  Paul Glendinning (2014) The Border Collision Normal Form with Stochastic Switching Surface. SIAM J. Applied Dynamical Systems 13, 181-193
-  P. Kowalczyk, S. Nema, P. Glendinning, I. Loram, and M. Brown (2014) "Auto-regressive moving average analysis of linear and discontinuous models of human balance during quiet standing." Chaos: An Interdisciplinary Journal of Nonlinear Science 24: 022101.
-  50 Visions of Mathematics (2014) Ed. Sam Parc [PG is the ‘P’], OUP.
-  M. Goodfellow and P. Glendinning (2013) Mechanisms of Intermittent State Transitions in a Coupled Heterogeneous Oscillator Model of Epilepsy, J. Math. Neuroscience, 3, 17 doi:10.1186/2190-8567-3-17
-  V. Botella-Soler, J.A. Oteo, J. Ros and P. Glendinning (2013) Lyapunov exponent and topological entropy plateaus in piecewise linear maps J. Phys. A: 46, 125101 [26 pages]
-  P. Glendinning and L.A. Smith (2013) Lacunarity and period-doubling, Dyn. Syst. IJ, DOI:10.1080/14689376.2012.755496 [11 pages]
-  P. Glendinning, P. Kowalczyk and A.B. Nordmark (2012) Attractors near grazing-sliding bifurcations, Nonlinearity 25 1867--1885.
-  P. Glendinning (2012) Maths In Minutes, Quercus. [410 small pages]
-  V. Botella-Soler and P. Glendinning (2012) Emergence of hierarchical networks and polysynchronous behaviour in simple adaptive systems, EPL, 97, 50004.
-  M. Pailha, A. L. Hazel, P. A. Glendinning, and A. Juel (2012) Oscillatory bubbles induced by geometrical constraint, Physics of Fluids, 24, 021702-1-021702-7
-  P. Kowalczyk, P. Glendinning, M. Brown, G. Medrano-Cerda, H. Dallali, J. Shapiro (2012) Modelling human balance using switched systems with linear feedback control, J Roy Soc Interfac, 9, 234-245.
-  P. Glendinning (2011) Two Ball Newton Cradle, Phys. Rev. E, 84:067201
-  K. Liao, R.M. Schneider, S.S. Yaniglos, G. Bertolini, P. Glendinning, R.N. Sawyer, Jr., M. Reschke, and R.J. Leigh (2011) Visual and vestibular determinants of the translational vestibulo-ocular reflex, Ann. NY Acad. Sci., 1233, 263-270.
-  P. Glendinning and P. Kowalczyk (2011) ‘Boundary-equilibrium bifurcations in piecewise-smooth slow-fast systems.’ Chaos. 21:023126 [11 pages].
-  R. Vitolo, P. Glendinning and J. Gallas (2011) ‘Global structure of periodicity hubs in Lyapunov phase diagrams of dissipative’, Phys. Rev. E 84, 016216 [7 pages]
-  P. Glendinning and C.H. Wong (2011) Two-dimensional attractors in the border-collision normal form, Nonlinearity, 24, 995-1010.
-  P. Glendinning (2010) Bifurcations of snap-back repellers with application to the border-collision normal form', Int. J. Bifn. Chaos 20, 479-489
-  P. Glendinning and P. Kowalczyk (2010) 'Micro-chaotic dynamics due to digital sampling in hybrid systems of Filippov type', Physica D, 239, 58-71
-  P. Glendinning and P. Kowalczyk (2009) 'Dynamics of a hybrid thermostat model with discrete sampling time control', Dynamical Systems IJ, 23 343-360.
-  P. Glendinning, T. Jaeger and J. Stark (2009) `Strangely dispersed minimal sets in the quasiperiodically forced Arnold circle map', Nonlinearity 22 835-854
-  'Border collision bifurcations, snap-back repellers, and chaos' (2009) Physical Review E (Vol.79, No.2): DOI: 10.1103/PhysRevE.79.025202 (with C.H. Wong).
-  ‘How chaotic are strange non-chaotic attractors?’ (2006) Nonlinearity, 19, 2005-2023 (with G.Keller and T.Jaeger).
-  'Routes to Chaos' (2005) Encyclopedia of Nonlinear Science
Ed A. Scott, Routledge, New York pp. 814-817.
-  'Invariant manifolds and sets' (2005) Encyclopedia of Nonlinear Science
Ed A. Scott, Routledge, New York pp. 465-467.
-  'Henon map' (2005) Encyclopedia of Nonlinear Science
Ed A. Scott, Routledge, New York pp. 403-406.
-  `The non-smooth pitchfork bifurcation' (2004)
Discrete and Continuous Dynamical Systems B 4, 457-464
(pdf file, 1.5M)
-  `The mathematics of motion camouflage' (2004) Proc. Roy. Soc. (London)
Series B 271 477-481 available as a pdf file.
-  `The accumulation of boundary doubling for modified tent maps' (2003)
Trends in Mathematics: Bifurcations, Symmetry and Patterns
Eds. J. Buescu, S.B.S.D. Castro, A.P.S. Dias \& I.S. Labouriau,
This note is available as a
-  `Stability of asymmetric cluster states in globally
coupled maps' (2003) Proceedings of the 2003
Workshop on Nonlinear Dynamics of Electronic Systems
ed. R. Stoop, 89-92, Universitat Zurich. This paper is available as a
-  `Global attractors of pinched skew products' (2002) Dyn. Syst. IJ
17 287-297. This paper is available as a
-  `Rotation numbers for quasi-periodically forced monotone circle maps'
(2002) Dyn. Sys. IJ 17 1-28 (with J. Stark, U. Feudel and A.S. Pikovsky).
A pdf version
of this paper can be downloaded here.
-  `Imperfect Homoclinic Bifurcations' (2001) Phys. Rev. E 64 036208
(8 pages) (with J. Abshagen and
-  `Multistability in the quasiperiodically forced circle
map' (2001) IJBC 11 3085-3105 (with H. Osinga, U. Feudel and J. Wiersig).
has its very own
web site which has loads of pretty pictures (in colour) and explanatory text.
-  `Unique representations of real numbers in non-integer bases' (2001)
Math. Res. Lett. 8 535-543 (with N. Sidorov).
A dvi file is available.
-  `Hyperbolicity of the invariant set for the logistic map with
mu > 4' (2001) Nonlinear Analysis: Theory, Methods & Applications 47
3323-3332. This note is basically pedagogical,
but contains a new and very simple proof of the result. It can be
downloaded as a dvi file.
-  From finite to infinite dimensional dynamical systems
(2001) Editor, with J.C. Robinson, and co-author of Introduction.
Kluwer NATO Science Series, II. Math., Phys.and Chem. 19, 215 pages.
-  `Milnor attractors and topological attractors in a piecewise
linear map' (2001) Nonlinearity 14 239-258. Available as a
-  `The structure of mode-locked regions in quasi-periodically forced
circle maps' (2000) Physica D 140 227-243 (with U. Feudel, A.S. Pikovsky and
J. Stark). This paper is available in
-  `Transitivity and blowout bifurcations in a class of globally
coupled maps' (1999) Phys. Lett. A 264 303-310
(pdf -- text only)
-  `The stability boundary of synchronized states in globally coupled
dynamical systems' (1999) Phys. Lett. A 259 129-134
-  `Fine structure of mode-locked regions of the quasi-periodically
forced circle map' (1999) Phys. Lett. A 257 65-69 (with J. Wiersig)
-  `Towards a quasi-periodic mean field theory of globally coupled
oscillators' (1999) Phys. Lett. A 251 297-302 (with M. Banaji)
-  `Intermittency and strange nonchaotic attractors in quasi-periodically
forced circle maps' (1998) Phys. Lett. A 244 545-550
-  `Melnikov analysis of chaos in a simple epidemiological model' (1997)
J. Math. Biol. 35 359-373 (with L.P. Perry)
-  `Bifocal homoclinic bifurcations' (1997) Physica D 102 1-14
(with C.R. Laing)
-  `Inaccessible attractors of weakly dissipative systems' (1997)
Nonlin. 10 507-522
-  `Differential equations with bifocal homoclinic orbits' (1997)
Intl. J. Bifn. & Chaos 727-37
-  `Shilnikov's saddle-node bifurcation' (1996) Intl. J. Bifn.
& Chaos 6 1153-1160 (with C. Sparrow)
-  `Zeros of the kneading invariant and topological entropy for
Lorenz maps' (1996) Nonlin. 9 999-1014 (with T. Hall)
-  `A homoclinic hierarchy' (1996) Phys. Lett. A 211 155-160
(with C.R. Laing)
-  `Bifurcations and rotation numbers for maps of the circle
associated with flows on the torus and models of cardiac arrythmias'
(1995) Dyn. Stab. Sys. 10 367-386
-  `Locating bifurcations in quasiperiodically forced systems' (1995)
Phys. Lett. A 200 17-26 (with P.R. Chastell and J. Stark)
-  Stability, Instability and Chaos: an introduction to the theory
of nonlinear differential equations (1994) 388 pages, CUP
-  `Island chain models and gradient systems' (1994)
J. Math. Biol. 32 171-178
-  `Prime and renormalisable kneading invariants and the dynamics of
expanding Lorenz maps' (1993) Physica D 62, 22-50 (with C. Sparrow)
-  `Travelling waves with spatially resonant forcing: bifurcations of a
modified Landau equation' (1993) Int. J. Bifn. & Chaos 3, 1447-1455 (with
-  `The anharmonic route to chaos: kneading theory' (1993) Nonlin.
-  `Robust new routes to chaos in differential equations' (1992)
Phys. Lett. A 168 40-46
-  `Time series near codimension two global bifurcations' (1990) in
Measures of complexity and chaos eds. N. Abraham, A. Albano,
A. Passamante and P. Rapp, Plenum
-  `Renormalisation between classes of maps' (1990) Phys. Lett. A
145 109-112 (with J.E. Los and C. Tresser)
-  `Explicit renormalisation of some piecewise linear maps' (1990)
Physica D 44 149-167 (with D. Veitch)
-  `Topological conjugation of Lorenz maps to $\beta$-transformations'
(1990) Math. Proc. Camb. Phil. Soc. 107, 401-413
-  `Global structure of homoclinic bifurcations: a combinatorial
approach' (1989) Phys. Lett. A 141 391-396
-  `Subsidiary bifurcations near bifocal homoclinic orbits' (1989)
Math. Proc. Camb. Phil. Soc.105 597-605
-  `Dynamique symbolique pour la renormalisation des endomorphismes
d'entropie nulle de l'intervalle' (1988) C. R. Acad. Sci. (Paris) S\'erie I
307 607-612 (with J.E. Los, M.V. Otero-Espinar and C. Tresser)
-  `The gluing bifurcation I: symbolic dynamics of the closed curves' (1988)
Nonlinearity 1, 203-214 (with J.M. Gambaudo and C. Tresser)
-  `Global bifurcations in flows' (1988) in
New directions in dynamical systems eds. T. Bedford and J. Swift, CUP
-  `Asymmetric perturbations of Lorenz-like equations' (1987) Dyn.Stab. Syst.
-  `Travelling waves near isolated double-pulse solutions of nerveaxon equations',
(1987) Phys. Lett. A 121, 411-413
-  `Homoclinic bifurcations in ordinary differential equations' (1987)
in Chaos in biological systems, eds. H. Degn, A.V. Holden and
L. Olson, Plenum, New York
-  `Stable cycles with complicated structures' (1987) in
Instabilitiesand nonequilibrium structures, eds. E. Tirapegui and D. Villarroel,
D.Reidel Publishing Co. (with J.M. Gambaudo and C. Tresser)
-  `T-points: a codimension two heteroclinic bifurcation' (1986)
J. Stat. Phys. 43, 479-488 (with C. Sparrow)
-  `Stable cycles with complicated structures' (1985) J. Physique Lett.
46, L653-L658 (with J.M. Gambaudo and C. Tresser)
-  `Heteroclinic loops leading to hyperchaos' (1985) J. Physique Lett.
46, L347-L352 (with J.M. Gambaudo and C. Tresser)
-  `Collage de cycles et suites de Farey' (1984) C.R. Acad. Sci. S\'erie I,
300, 311-313 (with J.M. Gambaudo and C. Tresser)
-  `The rotation interval as a computable measure of chaos' (1984)
Phys. Lett. A 105, 97-100 (with J.M. Gambaudo and C. Tresser)
-  `Bifurcations near homoclinic orbits with symmetry' (1984) Phys.Lett. A
-  `Local and global behaviour near homoclinic orbits' (1984) J. Stat. Phys. 35,
645-696 (with C. Sparrow)
Lecture notes/theses/books in progress
-  `Homoclinic bifurcation' (1985) Ph.D. thesis, University of Cambridge
-  `Introduction to computational dynamics` (1988) lecture notes,
112 pages, for ICTP Summer School on Dynamical Systems, Trieste, 1988
(with J. Stark)
-  Chaos and routes to chaos in Lorenz maps (1992) an essay for the
Adams Prize (223 pages), to become a book
-  Flow instability, chaos and turbulence (1993)
lecture notes for
industrial education programme at the Newton Institute (with H.K. Moffatt
and M.R.E. Proctor)
-  Bifurcation Theory: codimension one bifurcations (1996) lecture
notes for Nonlinear Mathematics School, Bristol
-  `Maps of the Circle' in One dimensional dynamics, (1996)
TEMPUS Lecture Notes volume 14
-  Mathematical models in economics (1998) Queen Mary and Westfield
College Lecture Notes, 115 pages, to become a book
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