Associate Professor Vivien Kirk

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Associate Professor


I studied Mathematics and Physics as an undergraduate at the University of Auckland, then completed an MSc in Physics at the University of Auckland and a PhD in Applied Mathematics at Cambridge University. I held postdoctoral research appointments at the University of California, Berkeley and at Caltech before returning to New Zealand to take up a position in the Mathematics Department at the University of Auckland.

Research | Current

My research is in the broad area of dynamical systems within applied mathematics. Dynamical systems is the study of the qualitative properties of mathematical systems (typically nonlinear differential equations) that change with time. My interests include bifurcation theory, especially global bifurcations and bifurcations with symmetry, and applications of dynamical systems theory to physics and biology. 

My recent work has mostly focused on applying dynamical systems ideas to mathematical models of systems with multiple time scales, i.e., to systems in which some processes occur much faster than others. The existence of multiple time scales is common in models arising from cell physiology; much of my recent work aims to explain the complex behaviour observed in models of intracellular calcium dynamics.

Teaching | Current

Semester 1, 2018

MATHS 260: Differential Equations

Semester 2, 2018

MATHS 340: Real and Complex Calculus

I also often teach MATHS 761: Dynamical Systems

Committees/Professional groups/Services

I am Associate Dean (Doctoral) in the Faculty of Science and serve on the Board of Gradiate Studies in the role. I also serve on the University Academic Staffing Committee and represent this committee on the Faculty of Arts Staffing Committee.

I am currently the President for the New Zealand Mathematical Society. 

Selected publications and creative works (Research Outputs)

  • Han, J. M., Tanimura, A., Kirk, V., & Sneyd, J. (2017). A mathematical model of calcium dynamics in HSY cells. PLoS Computational Biology, 13 (2)10.1371/journal.pcbi.1005275
    Other University of Auckland co-authors: James Sneyd
  • Sneyd, J., Han, J. M., Wang, L., Chen, J., Yang, X., Tanimura, A., ... Yule, D. I. (2017). On the dynamical structure of calcium oscillations. Proceedings of the National Academy of Sciences of the United States of America, 114 (7), 1456-1461. 10.1073/pnas.1614613114
    Other University of Auckland co-authors: James Sneyd
  • Farjami, S., Kirk, V., & Osinga, H. M. (2016). Transient spike adding in the presence of equilibria. European Physical Journal: Special Topics, 225 (13-14), 2601-2612. 10.1140/epjst/e2015-50332-9
    Other University of Auckland co-authors: Hinke Osinga
  • Dupont, G., Falcke, M., Kirk, V., & Sneyd, J. (2016). Models of Calcium Signalling. Springer. Pages: 436.
    Other University of Auckland co-authors: James Sneyd
  • Boie, S., Kirk, V., Sneyd, J., & Wechselberger, M. (2016). Effects of quasi-steady-state reduction on biophysical models with oscillations. Journal of Theoretical Biology, 393, 16-31. 10.1016/j.jtbi.2015.12.011
    Other University of Auckland co-authors: James Sneyd
  • Nan, P., Wang, Y., Kirk, V., & Rubin, J. E. (2015). Understanding and distinguishing three-time-scale oscillations: Case study in a coupled Morris–Lecar system. SIAM Journal on Applied Dynamical Systems, 14 (3), 1518-1557. 10.1137/140985494
  • Kirk, V. J., & Sneyd, A. (2015). The nonlinear dynamics of calcium. Mathematical analysis of complex cellular activity (pp. 53-107). Springer International Publishing. 10.1007/978-3-319-18114-1_2
    Other University of Auckland co-authors: James Sneyd
  • Chen, X., Iremonger, K., Herbison, A., Kirk, V., & Sneyd, J. (2013). Regulation of Electrical Bursting in a Spatiotemporal Model of a GnRH Neuron. Bulletin of Mathematical Biology, 75 (10), 1941-1960. 10.1007/s11538-013-9877-7


Contact details

Primary office location

SCIENCE CENTRE 303 - Bldg 303
Level 2, Room 225
New Zealand

Web links