Journal
Simpson, DJW., & Glendinning, PA. (2024). Inclusion of higher-order terms in the border-collision normal form: Persistence of chaos and applications to power converters.
Physica D: Nonlinear Phenomena. 462
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Simpson, DJW. (2024). The necessity of the sausage-string structure for mode-locking regions of piecewise-linear maps.
Physica D: Nonlinear Phenomena. 462
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Simpson, DJW. (2024). Border-collision bifurcations from stable fixed points to any number of coexisting chaotic attractors.
Journal of Difference Equations and Applications. 30(1), 90-110
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Glendinning, PA., & Simpson, DJW. (2023). Unstable dimension variability and heterodimensional cycles in the border-collision normal form.
Physical Review E. 108(2)
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Fatoyinbo, HO., & Simpson, DJW. (2023). A Synopsis of the Noninvertible, Two-Dimensional, Border-Collision Normal Form with Applications to Power Converters.
International Journal of Bifurcation and Chaos. 33(8)
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Jeffrey, MR., Piiroinen, PT., & Simpson, DJW. (2023). Preface to VSI: Advances in nonsmooth dynamics.
Physica D: Nonlinear Phenomena. 453
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Glendinning, PA., & Simpson, DJW. (2023). NORMAL FORMS, DIFFERENTIABLE CONJUGACIES, AND ELEMENTARY BIFURCATIONS OF MAPS.
SIAM Journal on Applied Mathematics. 83(2), 816-836
[Journal article]Authored by: Simpson, D.Read Online:
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Belykh, I., Kuske, R., Porfiri, M., & Simpson, DJW. (2023). Beyond the Bristol book: Advances and perspectives in non-smooth dynamics and applications.
Chaos. 33(1)
[Journal article]Authored by: Simpson, D.Edited by: Simpson, D.Read Online:
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Simpson, DJW. (2023). Detecting invariant expanding cones for generating word sets to identify chaos in piecewise-linear maps.
Journal of Difference Equations and Applications. 29(9-12), 1094-1126
[Journal article]Authored by: Simpson, D.Read Online:
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Muni, SS., McLachlan, RI., & Simpson, DJW. (2022). UNFOLDING GLOBALLY RESONANT HOMOCLINIC TANGENCIES.
Discrete and Continuous Dynamical Systems- Series A. 42(8), 4013-4030
[Journal article]Authored by: McLachlan, R., Simpson, D.Read Online:
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Glendinning, PA., & Simpson, DJW. (2022). Normal forms for saddle-node bifurcations: Takens' coefficient and applications in climate models.
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 478(2267)
[Journal article]Authored by: Simpson, D.Read Online:
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Ghosh, I., & Simpson, DJW. (2022). Renormalization of the Two-Dimensional Border-Collision Normal Form.
International Journal of Bifurcation and Chaos. 32(12)
[Journal article]Authored by: Simpson, D.Read Online:
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Glendinning, PA., & Simpson, DJW. (2022). Chaos in the border-collision normal form: A computer-assisted proof using induced maps and invariant expanding cones.
Applied Mathematics and Computation. 434
[Journal article]Authored by: Simpson, D.Read Online:
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Simpson, DJW. (2022). Twenty Hopf-like bifurcations in piecewise-smooth dynamical systems.
Physics Reports. 970, 1-80
[Journal article]Authored by: Simpson, D.Read Online:
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Fatoyinbo, HO., Brown, RG., Simpson, DJW., & van Brunt, B. (2022). Pattern Formation in a Spatially Extended Model of Pacemaker Dynamics in Smooth Muscle Cells.
Bulletin of Mathematical Biology. 84(8)
[Journal article]Authored by: Brown, R., Simpson, D., Van Brunt, B.Read article at Massey Research Online:
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Simpson, DJW. (2022). Dimension reduction for slow-fast, piecewise-linear ODEs and obstacles to a general theory.
Physica D: Nonlinear Phenomena. 439
[Journal article]Authored by: Simpson, D.Read Online:
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Ghosh, I., & Simpson, DJW. (2022). Robust Devaney chaos in the two-dimensional border-collision normal form.
Chaos. 32(4)
[Journal article]Authored by: Simpson, D.Read Online:
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Simpson, DJW. (2021). On the stability of boundary equilibria in filippov systems.
Communications on Pure and Applied Analysis. 20(9), 3075-3093
[Journal article]Authored by: Simpson, D.Read Online:
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Muni, SS., McLachlan, RI., & Simpson, DJW. (2021). Homoclinic tangencies with infinitely many asymptotically stable single-round periodic solutions.
Discrete and Continuous Dynamical Systems- Series A. 41(8), 3629-3650
[Journal article]Authored by: McLachlan, R., Simpson, D.Read Online:
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Glendinning, PA., & Simpson, DJW. (2021). A constructive approach to robust chaos using invariant manifolds and expanding cones.
Discrete and Continuous Dynamical Systems- Series A. 41(7), 3367-3387
[Journal article]Authored by: Simpson, D.Read Online:
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Simpson, DJW. (2020). Chaotic attractors from border-collision bifurcations: Stable border fixed points and determinant-based lyapunov exponent bounds..
New Zealand Journal of Mathematics. 50, 71-91
[Journal article]Authored by: Simpson, D.Read Abstract:
Simpson, DJW., Avrutin, V., & Banerjee, S. (2020). Nordmark map and the problem of large-amplitude chaos in impact oscillators.
Physical Review E. 102(2)
[Journal article]Authored by: Simpson, D.Read Online:
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Fatoyinbo, HO., Brown, RG., Simpson, DJW., & van Brunt, B. (2020). Numerical Bifurcation Analysis of Pacemaker Dynamics in a Model of Smooth Muscle Cells.
Bulletin of Mathematical Biology. 82(7)
[Journal article]Authored by: Brown, R., Simpson, D., Van Brunt, B.Read Online:
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Simpson, DJW. (2020). Unfolding Codimension-Two Subsumed Homoclinic Connections in Two-Dimensional Piecewise-Linear Maps.
International Journal of Bifurcation and Chaos. 30(3)
[Journal article]Authored by: Simpson, D.Read Online:
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Simpson, DJW. (2020). The Stability of Fixed Points on Switching Manifolds of Piecewise-Smooth Continuous Maps.
Journal of Dynamics and Differential Equations. 32(3), 1527-1552
[Journal article]Authored by: Simpson, D.Read Online:
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Al Fran, HA., Simpson, DJW., & Tuffley, CP. (2019). Characterisation and classification of signatures of spanning trees of the n-cube.
Australasian Journal of Combinatorics. 75(3), 259-295
[Journal article]Authored by: Simpson, D., Tuffley, C.Read Abstract:
Simpson, DJW. (2019). Hopf-like boundary equilibrium bifurcations involving two foci in Filippov systems.
Journal of Differential Equations. 267(11), 6133-6151
[Journal article]Authored by: Simpson, D.Read Online:
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Simpson, DJW. (2018). A general framework for boundary equilibrium bifurcations of Filippov systems.
Chaos. 28(10)
[Journal article]Authored by: Simpson, D.Read Online:
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Simpson, DJW. (2018). A compendium of Hopf-like bifurcations in piecewise-smooth dynamical systems.
Physics Letters, Section A: General, Atomic and Solid State Physics. 382(35), 2439-2444
[Journal article]Authored by: Simpson, D.Read Online:
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Jeffrey, MR., Kafanas, G., & Simpson, DJW. (2018). Jitter in Piecewise-Smooth Dynamical Systems with Intersecting Discontinuity Surfaces.
International Journal of Bifurcation and Chaos. 28(6)
[Journal article]Authored by: Simpson, D.Read Online:
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Simpson, DJW. (2018). The structure of mode-locking regions of piecewise-linear continuous maps: II. Skew sawtooth maps.
Nonlinearity. 31(5), 1905-1939
[Journal article]Authored by: Simpson, D.Read Online:
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Simpson, DJW., & Kuske, R. (2018). The influence of localized randomness on regular grazing bifurcations with applications to impacting dynamics.
JVC/Journal of Vibration and Control. 24(2), 407-426
[Journal article]Authored by: Simpson, D.Read Online:
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Simpson, DJW. (2017). Grazing-Sliding Bifurcations Creating Infinitely Many Attractors.
International Journal of Bifurcation and Chaos. 27(12)
[Journal article]Authored by: Simpson, D.Read Online:
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Simpson, DJW. (2017). Open problems on border-collision bifurcations.
Trends in Mathematics. 8, 163-166
[Journal article]Authored by: Simpson, D.Read Online:
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Simpson, DJW., & Tuffley, CP. (2017). Subsumed Homoclinic Connections and Infinitely Many Coexisting Attractors in Piecewise-Linear Maps.
International Journal of Bifurcation and Chaos. 27(2)
[Journal article]Authored by: Simpson, D., Tuffley, C.Read Online:
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Simpson, DJW. (2017). The structure of mode-locking regions of piecewise-linear continuous maps: I. Nearby mode-locking regions and shrinking points.
Nonlinearity. 30(1), 382-444
[Journal article]Authored by: Simpson, D.Read Online:
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Simpson, DJW. (2016). Unfolding homoclinic connections formed by corner intersections in piecewise-smooth maps.
Chaos. 26(7)
[Journal article]Authored by: Simpson, D.Read Online:
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Simpson, DJW. (2016). Border-collision bifurcations in R<sup>N</sup>.
SIAM Review. 58(2), 177-226
[Journal article]Authored by: Simpson, D.Read Online:
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Simpson, DJW. (2016). The instantaneous local transition of a stable equilibrium to a chaotic attractor in piecewise-smooth systems of differential equations.
Physics Letters, Section A: General, Atomic and Solid State Physics. 380(38), 3067-3072
[Journal article]Authored by: Simpson, D.Read Online:
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Simpson, DJW., & Jeffrey, MR. (2016). Fast phase randomization via two-folds.
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 472(2186)
[Journal article]Authored by: Simpson, D.Read Online:
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Simpson, DJW., & Kuske, R. (2015). Stochastic Perturbations of Periodic Orbits with Sliding.
Journal of Nonlinear Science. 25(4), 967-1014
[Journal article]Authored by: Simpson, D.Read Online:
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Simpson, DJW., & Kuske, R. (2014). The positive occupation time of Brownian motion with two-valued drift and asymptotic dynamics of sliding motion with noise.
Stochastics and Dynamics. 14(4)
[Journal article]Authored by: Simpson, D.Read Online:
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Simpson, DJW. (2014). Review of "Brownian Dynamics at Boundaries and Interfaces: In Physics, Chemistry, and Biology" by Zeev Schuss..
SIAM Review. 56(4), 722-723
[Book Review]Authored by: Simpson, D.Simpson, DJW. (2014). Scaling laws for large numbers of coexisting attracting periodic solutions in the border-collision normal form.
International Journal of Bifurcation and Chaos. 24(9)
[Journal article]Authored by: Simpson, D.Read Online:
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Simpson, DJW., & Kuske, R. (2014). Stochastically perturbed sliding motion in piecewise-smooth systems.
Discrete and Continuous Dynamical Systems - Series B. 19(9), 2889-2913
[Journal article]Authored by: Simpson, D.Read Online:
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Simpson, DJW. (2014). On the relative coexistence of fixed points and period-two solutions near border-collision bifurcations.
Applied Mathematics Letters. 38, 162-167
[Journal article]Authored by: Simpson, D.Read Online:
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Simpson, DJW. (2014). Sequences of periodic solutions and infinitely many coexisting attractors in the border-collision normal form.
International Journal of Bifurcation and Chaos. 24(6)
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Simpson, DJW. (2014). On resolving singularities of piecewise-smooth discontinuous vector fields via small perturbations.
Discrete and Continuous Dynamical Systems- Series A. 34(9), 3803-3830
[Journal article]Authored by: Simpson, D.Read Online:
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Jeffrey, MR., & Simpson, DJW. (2014). Non-Filippov dynamics arising from the smoothing of nonsmooth systems, and its robustness to noise.
Nonlinear Dynamics. 76(2), 1395-1410
[Journal article]Authored by: Simpson, D.Read Online:
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Simpson, DJW., Hogan, SJ., & Kuske, R. (2013). Stochastic regular grazing bifurcations.
SIAM Journal on Applied Dynamical Systems. 12(2), 533-559
[Journal article]Authored by: Simpson, D.Read Online:
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Simpson, DJW., & Meiss, JD. (2012). Aspects of bifurcation theory for piecewise-smooth, continuous systems.
Physica D: Nonlinear Phenomena. 241(22), 1861-1868
[Journal article]Authored by: Simpson, D.Read Online:
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Simpson, DJW., Kuske, R., & Li, YX. (2012). Dynamics of simple balancing models with time-delayed switching feedback control.
Journal of Nonlinear Science. 22(2), 135-167
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Simpson, DJW., & Kuske, R. (2011). Mixed-mode oscillations in a stochastic, piecewise-linear system.
Physica D: Nonlinear Phenomena. 240(14-15), 1189-1198
[Journal article]Authored by: Simpson, D.Read Online:
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Simpson, DJW., & Meiss, JD. (2011). Aspects of bifurcation theory for piecewise-smooth, continuous systems.
Physica D: Nonlinear Phenomena.
[Journal article]Authored by: Simpson, D.Read Abstract:
Simpson, DJW., & Meiss, JD. (2010). Resonance near border-collision bifurcations in piecewise-smooth, continuous maps.
Nonlinearity. 23(12), 3091-3118
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Simpson, DJW., & Meiss, JD. (2009). Shrinking point bifurcations of resonance tongues for piecewise-smooth, continuous maps.
Nonlinearity. 22(5), 1123-1144
[Journal article]Authored by: Simpson, D.Read Online:
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Simpson, DJW., & Meiss, JD. (2009). Simultaneous border-collision and period-doubling bifurcations.
Chaos. 19(3)
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Simpson, DJW., Kompala, DS., & Meiss, JD. (2009). Discontinuity induced bifurcations in a model of Saccharomyces cerevisiae.
Mathematical Biosciences. 218(1), 40-49
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Simpson, DJW., & Meisst, JD. (2008). Neimark-Sacker bifurcations in planar, piecewise-smooth, continuous maps.
SIAM Journal on Applied Dynamical Systems. 7(3), 795-824
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Simpson, DJW., & Meiss, JD. (2008). Unfolding a codimension-two, discontinuous, Andronov-Hopf bifurcation.
Chaos. 18(3)
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Marts, B., Simpson, DJW., Hagberg, A., & Lin, AL. (2007). Period doubling in a periodically forced Belousov-Zhabotinsky reaction.
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. 76(2)
[Journal article]Authored by: Simpson, D.Read Online:
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Simpson, DJW., & Meiss, JD. (2007). Andronov-Hopf bifurcations in planar, piecewise-smooth, continuous flows.
Physics Letters, Section A: General, Atomic and Solid State Physics. 371(3), 213-220
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Simpson, DJ., Kirk, V., & Sneyd, J. (2005). Complex Oscillations and Waves of Calcium in Pancreatic Acinar Cells.
Physica D-Nonlinear Phenomena. 200, 303-324
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Conference
Glendinning, P., & Simpson, DJW.Differentiable Conjugacies for One-Dimensional Maps.
Springer Proceedings in Mathematics and Statistics. (pp. 115 - 130). 2194-1009.
[Conference]Authored by: Simpson, D.Read Online:
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Fatoyinbo, HO., Brown, RG., Simpson, DJW., & Van Brunt, B. (2022). EFFECTS OF CONDUCTANCE OF ION CHANNELS ON SPONTANEOUS ELECTRICAL ACTIVITY IN SMOOTH MUSCLES. , 13th INTERNATIONAL CONFERENCE DYNAMICAL SYSTEMS APPLIED TO BIOLOGY AND NATURAL SCIENCES (DSABNS)
[Conference Abstract]Authored by: Simpson, D., Van Brunt, B.Read Abstract:
Simpson, DJW. (2017, May). Desynchronising collections of oscillators by using two-fold singularities. Presented at
SIAM Conference on Applications of Dynamical Systems. Snowbird, UT, USA.
[Conference Oral Presentation]Authored by: Simpson, D.Simpson, DJW. (2016, June). Using two-fold singularities to desynchronise collections of oscillators. Presented at
School/Workshop on Applicable Theory of Switched Systems. The University of Texas at Dallas, Dallas, TX, USA.
[Conference Oral Presentation]Authored by: Simpson, D.Simpson, DJW. (2016, February). Noisy sliding motion and a probabilistic notion of forward evolution through a two-fold. Presented at
Intensive Research Programme on Advances in Nonsmooth Dynamics
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Simpson, DJW. (2016, February). Border-Collision Bifurcations: Myths, Facts and Open Problems. Presented at
Intensive Research Programme on Advances in Nonsmooth Dynamics. CRM, Barcelona, Spain.
[Conference Oral Presentation]Authored by: Simpson, D.Simpson, DJW. (2015, May). Infinitely many coexisting attractors in the border-collision normal form.. Presented at
SIAM Conference on Applied Dynamical Systems. Snowbird, Utah, USA.
[Conference Oral Presentation]Authored by: Simpson, D.Simpson, DJW. (2014, February). Effects of Noise on Nonsmooth Dynamical Systems. Presented at
ANZIAM 2014. Rotorua, NZ.
[Conference Oral Presentation]Authored by: Simpson, D.Simpson, DJW. (2013, November). Probabilistic Forward Evolution through Singularities of Discontinuous Vector Fields. Presented at
16th Manuwatu-Wellington Applied Maths Day. Victoria University, Wellington, NZ.
[Conference Oral Presentation]Authored by: Simpson, D.Simpson, DJW. (2013, May). Stochastic Grazing Bifurcations. Presented at
SIAM Conference on Applications of Dynamical Systems. Snowbird, UT, USA.
[Conference Oral Presentation]Authored by: Simpson, D.Simpson, DJW. (2013, December). Probabilistic Forward Evolution through Singularities of Discontinuous Vector Fields. Presented at
NZMS Colloquium. Tauranga, NZ.
[Conference Oral Presentation]Authored by: Simpson, D.Simpson, DJW. (2012, November). Dynamics of a Prototypical Balancing Model with Switching Control. Presented at
15th Manuwatu-Wellington Applied Maths Day. Massey University, Palmerston North, NZ.
[Conference Oral Presentation]Authored by: Simpson, D.Simpson, DJW. (2012, January). Noisy Sliding Motion. Presented at
Maps, Gaps and Noise Workshop. University of Bath, England.
[Conference Oral Presentation]Authored by: Simpson, D.Simpson, DJW. (2012, July). The Effects of Noise on Sliding Motion. Presented at
The 9th AIMS Conference on Dynamical Systems, Differential Equations and Applications. Orlando, FL, USA.
[Conference Oral Presentation]Authored by: Simpson, D.Simpson, DJW. (2012, December). Resonance in Piecewise-Smooth Continuous Maps. Presented at
NZMS Colloquium. Massey University, Palmerston North, NZ.
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