Dr David Simpson staff profile picture

Contact details +64 (06) 356 9099  ext. 84618

Dr David Simpson MSc Auck., PhD Colorado

Senior Lecturer in Mathematics

Institute of Fundamental Sciences

Professional

Qualifications

  • Bachelor of Science (Mathematics & Statistics) - University of Auckland (2002)
  • Master of Science (Applied Mathematics) - University of Auckland (2004)
  • Doctor of Philosophy (Applied Mathematics) - University of Colorado at Boulder (2008)

Prizes and Awards

  • Massey University International Visitors Research Fund. I was awarded $2976 to host Paul Glendinning from the University of Manchester. Paul Glendinning is a world-renowned expect in dynamical systems. He is currently the scientific director of the International Centre for Mathematical Sciences based in Edinburgh, was the head of the School of Mathematics at The University of Manchester in the 2000's, and has written books on dynamical systems and popular science. He visited me at Massey University from May 4 -- May 19, 2017 for collaborative research on robust chaos. - Massey University (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

Summary of Research Projects

Position Current Completed
Project Leader 0 1

Research Outputs

Journal

Simpson, DJW. (2017). Open problems on border-collision bifurcations. Trends in Mathematics. 8, 163-166
[Journal article]Authored by: Simpson, D.
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.
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.
Simpson, DJW. (2016). Unfolding homoclinic connections formed by corner intersections in piecewise-smooth maps. Chaos. 26(7)
[Journal article]Authored by: Simpson, D.
Simpson, DJW. (2016). Border-collision bifurcations in R<sup>N</sup>. SIAM Review. 58(2), 177-226
[Journal article]Authored by: Simpson, D.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Simpson, DJW., & Meiss, JD. (2011). Aspects of bifurcation theory for piecewise-smooth, continuous systems. Physica D: Nonlinear Phenomena.
[Journal article]Authored by: Simpson, D.
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.
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.
Simpson, DJW., & Meiss, JD. (2009). Simultaneous border-collision and period-doubling bifurcations. Chaos. 19(3)
[Journal article]Authored by: Simpson, D.
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.
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.
Simpson, DJW., & Meiss, JD. (2008). Unfolding a codimension-two, discontinuous, Andronov-Hopf bifurcation. Chaos. 18(3)
[Journal article]Authored by: Simpson, D.
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.
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.
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.

Conference

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
[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. 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.
[Conference Oral Presentation]Authored by: Simpson, D.

Other

Simpson, DJW. (2016, July). Phase randomisation and other aspects of noisy nonsmooth systems. Presented at Massey University, 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 Massey University, Palmertston North, NZ.
[Oral Presentation]Authored by: Simpson, D.
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 Massey University, 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.

Supervision and Teaching

Summary of Doctoral Supervision

Position Current Completed
CoSupervisor 3 0

Current Doctoral Supervision

CoSupervisor of:

Media and Links

Other Links

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