Associate Professor Vivien Kirk

PhD (Cambridge), FNZMS

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Associate Professor

Research | Current

  • Dynamical systems
  • Bifurcation theory
  • Mathematical biology
  • Systems with multiple time scales
  • Dynamical systems with symmetry

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 2, 2019

MATHS 260: Differential Equations

MATHS 761: Dynamical Systems

Postgraduate supervision

Current students supervised or co-supervised:

  • Ielyaas Cloete (PhD)
  • Gray Manicom (PhD) 
  • Nathan Pages (PhD)
  • Xueshan Yang (PhD)
  • Morgan Meertens (MSc)

Project topics available:

  • Dynamical systems theory, particularly applications to systems with multiple time scales and models arising in intracellular calcium dynamics
  • Bifurcation theory
  • The dynamics of heteroclinic cycles and networks in systems with symmetry

Responsibilities

I am Associate Dean (Doctoral) in the Faculty of Science and serve on the Board of Gradiate Studies in the role. 

Committees/Professional groups/Services

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

I serve as an Associate Editor for the journals SIAM Journal on Applications of Dynamical Systems, Dynamical Systems - an International Journal, and the NZ Journal of Mathematics.

Selected publications and creative works (Research Outputs)

  • Pages, N., Vera-Sigüenza E, Rugis, J., Kirk, V., Yule, D. I., & Sneyd, J. (2019). A Model of [Formula: see text] Dynamics in an Accurate Reconstruction of Parotid Acinar Cells. Bulletin of mathematical biology, 81 (5), 1394-1426. 10.1007/s11538-018-00563-z
  • Desroches, M., & Kirk, V. (2018). Spike-Adding in a Canonical Three-Time-Scale Model: Superslow Explosion and Folded-Saddle Canards. SIAM Journal on Applied Dynamical Systems, 17 (3), 1989-2017. 10.1137/17M1143411
  • Farjami, S., Kirk, V., & Osinga, H. M. (2018). Computing the Stable Manifold of a Saddle Slow Manifold. SIAM Journal on Applied Dynamical Systems, 17 (1), 350-379. 10.1137/17M1132458
    Other University of Auckland co-authors: Hinke Osinga
  • 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
  • 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

Identifiers

Contact details

Office hours

For Semester 2 2019:

Mondays 3-4, Wednedays 2-3, Thursdays 3-4

Primary office location

SCIENCE CENTRE 303 - Bldg 303
Level 2, Room 225
38 PRINCES ST
AUCKLAND CENTRAL
AUCKLAND 1010
New Zealand

Web links