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Associate Professor David Simpson staff profile picture

Contact details +6469517618

Associate Professor David Simpson

Associate Professor in Mathematics

Doctoral Supervisor
School of Mathematical and Computational Sciences

Professional

Contact details

  • Ph: 06 951 7618
    Location: ScB3.07, Science Tower B
    Campus: Manawatu

Certifications and Registrations

  • Licence, Supervisor, 羞羞视频

Prizes and Awards

  • 羞羞视频 International Visitors Research Fund. - 羞羞视频 (2017)

Research Expertise

Research Interests

My research is in the broad area of dynamical systems. I have worked on a wide range of applications including mechanical systems with impacts or friction, relay control, human balancing tasks, excitable dynamics in neurons, the Belousov-Zhabotinsky chemical reaction, yeast growth, and calcium propagation in cells.

I am most interested in mathematical models for which the equations are nonsmooth (corresponding to some sort of switch, decision or impact). The behaviour of nonsmooth systems is often complicated and poorly understood because nonsmooth systems are highly nonlinear, and consequently can exhibit intricate and chaotic dynamics.

Thematics

21st Century Citizenship

Area of Expertise

Field of research codes
Applied Mathematics (010200): Biological Mathematics (010202): Dynamical Systems in Applications (010204): Mathematical Sciences (010000): Ordinary Differential Equations, Difference Equations and Dynamical Systems (010109): Pure Mathematics (010100): Statistics (010400): Stochastic Analysis and Modelling (010406)

Research Projects

Current Projects

Project Title: Minimal mathematical models for dynamical systems with abrupt events.

By determining how objects, fluids, organisms, etc, move we can predict their future state. We can then modify our actions or the system itself to our advantage, and in many ways this is the basis of technological advances throughout society. While some understanding can be achieved experimentally, to determine, quantitatively, what features cause which phenomena to occur and when, one needs a model. Through modelling we can explain how different dynamics occurs under different conditions. This can be achieved by analysing minimal models (normal forms) that describe critical changes (e.g. tipping points). However, for systems with collisions, thresholds, on/off control strategies, or other abrupt events, normal forms often fail to capture key elements of the dynamics. This project will explain when and why standard normal forms can be used and how to modify and simplify them when needed. The results will be based upon new geometric techniques for establishing when the dynamics is robust to variations in model parameters, and applied to characterise the occurrence and intensity of contact events that cause unwanted damage in mechanical systems. Overall the results will provide a rigorous methodology for determining how the physical features of a system drive its dynamics.
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Date Range: 2023 - 2026

Funding Bodies: Marsden Fund - Full; Royal Society of New Zealand

Project Team:

Completed Projects

Project Title: Organised chaos: Using geometry to explain robust chaotic dynamics in switched dynamical systems

Date Range: 2019 - 2024

Funding Body: Royal Society of New Zealand

Project Team:

Research Outputs

Journal

Simpson, DJW. (2025). A Piecewise-Linear Fixed Point Theorem. American Mathematical Monthly. 132(7), 695-699
[Journal article]Authored by: Simpson, D.
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Simpson, DJW. (2025). Three forms of dimension reduction for border-collision bifurcations. Physics Letters Section A General Atomic and Solid State Physics. 550
[Journal article]Authored by: Simpson, D.
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Simpson, DJW. (2025). Nonsmooth folds as tipping points. Chaos. 35(2)
[Journal article]Authored by: Simpson, D.
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1
Ghosh, I., McLachlan, RI., & Simpson, DJW. (2025). Robust Chaos in Orientation-Reversing and Non-Invertible Two-Dimensional Piecewise-Linear Maps. Journal of Nonlinear Science. 35(1)
[Journal article]Authored by: McLachlan, R., Simpson, D.
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Ghosh, I., McLachlan, RI., & Simpson, DJW. (2024). The bifurcation structure within robust chaos for two-dimensional piecewise-linear maps. Communications in Nonlinear Science and Numerical Simulation. 134
[Journal article]Authored by: McLachlan, R., Simpson, D.
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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
[Journal article]Authored by: Simpson, D.
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1
Simpson, DJW. (2024). The necessity of the sausage-string structure for mode-locking regions of piecewise-linear maps. Physica D Nonlinear Phenomena. 462
[Journal article]Authored by: Simpson, D.
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1
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
[Journal article]Authored by: Simpson, D.
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3
Glendinning, PA., & Simpson, DJW. (2023). Unstable dimension variability and heterodimensional cycles in the border-collision normal form. Physical Review E. 108(2)
[Journal article]Authored by: Simpson, D.
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1
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)
[Journal article]Authored by: Simpson, D.
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Jeffrey, MR., Piiroinen, PT., & Simpson, DJW. (2023). Preface to VSI: Advances in nonsmooth dynamics. Physica D Nonlinear Phenomena. 453
[Journal article]Authored by: Simpson, D.
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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.
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1
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.
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23
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.
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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.
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4
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.
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3
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.
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1
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.
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9
Simpson, DJW. (2022). Twenty Hopf-like bifurcations in piecewise-smooth dynamical systems. Physics Reports. 970, 1-80
[Journal article]Authored by: Simpson, D.
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19
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.
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3
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.
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6
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.
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10
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.
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2
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.
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9
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.
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15
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.
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2
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.
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13
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.
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9
3
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.
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9
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.
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6
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.
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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.
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13
Simpson, DJW. (2018). A general framework for boundary equilibrium bifurcations of Filippov systems. Chaos. 28(10)
[Journal article]Authored by: Simpson, D.
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15
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.
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31
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.
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15
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.
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9
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.
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13
Simpson, DJW. (2017). Grazing-Sliding Bifurcations Creating Infinitely Many Attractors. International Journal of Bifurcation and Chaos. 27(12)
[Journal article]Authored by: Simpson, D.
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14
Simpson, DJW. (2017). Open problems on border-collision bifurcations. Trends in Mathematics. 8, 163-166
[Journal article]Authored by: Simpson, D.
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3
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.
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9
3
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.
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18
Simpson, DJW. (2016). Unfolding homoclinic connections formed by corner intersections in piecewise-smooth maps. Chaos. 26(7)
[Journal article]Authored by: Simpson, D.
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9
Simpson, DJW. (2016). Border-collision bifurcations in RN. SIAM Review. 58(2), 177-226
[Journal article]Authored by: Simpson, D.
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50
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.
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10
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.
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3
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.
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10
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.
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2
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.
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17
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.
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14
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.
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7
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)
[Journal article]Authored by: Simpson, D.
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37
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.
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8
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.
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9
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.
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25
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.
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42
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
[Journal article]Authored by: Simpson, D.
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9
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.
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35
Simpson, DJW., & Meiss, JD. (2011). Aspects of bifurcation theory for piecewise-smooth, continuous systems. Physica D: Nonlinear Phenomena.
[Journal article]Authored by: Simpson, D.
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Simpson, DJW., & Meiss, JD. (2010). Resonance near border-collision bifurcations in piecewise-smooth, continuous maps. Nonlinearity. 23(12), 3091-3118
[Journal article]Authored by: Simpson, D.
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16
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.
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38
Simpson, DJW., & Meiss, JD. (2009). Simultaneous border-collision and period-doubling bifurcations. Chaos. 19(3)
[Journal article]Authored by: Simpson, D.
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14
Simpson, DJW., Kompala, DS., & Meiss, JD. (2009). Discontinuity induced bifurcations in a model of Saccharomyces cerevisiae. Mathematical Biosciences. 218(1), 40-49
[Journal article]Authored by: Simpson, D.
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14
Simpson, DJW., & Meisst, JD. (2008). Neimark-Sacker bifurcations in planar, piecewise-smooth, continuous maps. SIAM Journal on Applied Dynamical Systems. 7(3), 795-824
[Journal article]Authored by: Simpson, D.
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55
Simpson, DJW., & Meiss, JD. (2008). Unfolding a codimension-two, discontinuous, Andronov-Hopf bifurcation. Chaos. 18(3)
[Journal article]Authored by: Simpson, D.
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12
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.
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12
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
[Journal article]Authored by: Simpson, D.
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52
Simpson, DJ., Kirk, V., & Sneyd, J. (2005). Complex Oscillations and Waves of Calcium in Pancreatic Acinar Cells. Physica D-Nonlinear Phenomena. 200, 303-324
[Journal article]Authored by: Simpson, D.

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Book

Simpson, DJW.(2010). Bifurcations in piecewise-smooth continuous systems.
[Authored Book]Authored by: Simpson, D.
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Conference

Simpson, DJW. (2025). How to Compute Multi-dimensional Stable and Unstable Manifolds of Piecewise-Linear Maps. Springer Proceedings in Mathematics and Statistics. Vol. 485 (pp. 1 - 14).
[Conference Paper in Published Proceedings]Authored by: Simpson, D.
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Glendinning, P., & Simpson, DJW. (2024). Differentiable Conjugacies for One-Dimensional Maps. Springer Proceedings in Mathematics and Statistics. Vol. 444 (pp. 115 - 130).
[Conference Paper in Published Proceedings]Authored by: Simpson, D.
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Fatoyinbo, HO., Brown, RG., Simpson, DJW., & Van Brunt, B. (2022). Effects of ion channels conductance on spontaneous electrical activity in smooth muscles. In Virtual 13th International Conference Dynamical Systems Applied to Biology and Natural Sciences (DSABNS) 2022 Book of Abstracts(pp. 142 - 142). , Virtual 13th International Conference Dynamical Systems Applied to Biology and Natural Sciences (DSABNS) 2022 Bilbao, Spain: Dynamical Systems Applied to Biology and Natural Sciences (DSABNS)
[Conference Abstract]Authored by: Simpson, D., Van Brunt, B.
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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.

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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
[Conference Oral Presentation]Authored by: Simpson, D.
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. 羞羞视频, 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. 羞羞视频, Palmerston North, NZ.
[Conference Oral Presentation]Authored by: Simpson, D.

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Other

Simpson, DJW. (2016, July). Phase randomisation and other aspects of noisy nonsmooth systems. Presented at 羞羞视频, Palmerston North, NZ.
[Oral Presentation]Authored by: Simpson, D.
Simpson, DJW. (2015). Piecewise-linear maps: intricate dynamics with explicit solvability. (pp. 8 - 10).
[Other]Authored by: Simpson, D.
Simpson, DJW. (2015, May). Noisy Sliding Motion.. Presented at University of Colorado, Boulder, Colorado.
[Oral Presentation]Authored by: Simpson, D.
Simpson, DJW. (2014). Basins of infinitely many attractors.
[Other]Authored by: Simpson, D.
Simpson, DJW. (2013, August). Stochastic Perturbations of Sliding Motion and Periodic Orbits with Sliding Segments. Presented at 羞羞视频, Palmertston North, NZ.
[Oral Presentation]Authored by: Simpson, D.

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Simpson, DJW. (2013, July). Stochastic Perturbations of Sliding Motion and Periodic Orbits with Sliding Segments. Presented at University of Bristol, England.
[Oral Presentation]Authored by: Simpson, D.
Simpson, DJW. (2012, January). Resonance in Piecewise-Smooth Continuous Maps. Presented at University of Bristol, Bristol, England.
[Oral Presentation]Authored by: Simpson, D.
Simpson, DJW. (2012, March). The Positive Occupation Time of Brownian Motion with Two-Valued Drift. Presented at University of British Columbia, Vancouver, Canada.
[Oral Presentation]Authored by: Simpson, D.
Simpson, DJW. (2012, September). Stochastic Regular Grazing Bifurcations: An Example of Noise in Piecewise-Smooth Systems. Presented at 羞羞视频, Palmerston North, NZ.
[Oral Presentation]Authored by: Simpson, D.
Simpson, DJW. (2012, October). Stochastic Regular Grazing Bifurcations. Presented at Victoria University, NZ.
[Oral Presentation]Authored by: Simpson, D.
Simpson, DJW. (2012, October). Stochastic Regular Grazing Bifurcations. Presented at University of Auckland, NZ.
[Oral Presentation]Authored by: Simpson, D.
Simpson, DJ. (2010). Bifurcations in Piecewise-Smooth Continuous Systems. World Scientific
[Other]Authored by: Simpson, D.
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Teaching and Supervision

Contact Supervisor

Summary of Doctoral Supervision

Position Current Completed
Main Supervisor 0 2
Co-supervisor 0 4

Completed Doctoral Supervision

Main Supervisor of:

  • 2024 - Indranil Ghosh - Doctor of Philosophy
    Robust chaos in piecewise-linear maps
  • 2022 - Sishu Muni - Doctor of Philosophy
    Globally resonant homoclinic tangencies

Co-supervisor of:

  • 2023 - Sidra Zafar - Doctor of Philosophy
    An equation-free approach for heterogeneous networks
  • 2021 - Hammed Fatoyinbo - Doctor of Philosophy
    Pattern Formation in Electrically Coupled Pacemaker Cells
  • 2020 - Christian Offen - Doctor of Philosophy
    Analysis of Hamiltonian boundary value problems and symplectic integration
  • 2017 - Howida Al Fran - Doctor of Philosophy
    The edge slide graph of the n-dimensional cube

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