Qualifications & Memberships
My core research is in the general area of dynamical systems. The subject is exciting because it is a meeting place for real applications, numerical computation and beautiful theorems. A lot of my work is on the probabilistic side of dynamical systems: this is called "ergodic theory", where one seeks to know about the statistical properties of complex systems. I have made significant contributions in "numerical ergodic theory": approximation of important dynamical objects on a computer, with confidence in the accuracy of the output, backed by mathematical rigour. Since joining the University of Canterbury I have worked with collaborators on applications in ecology, energy, finance and physiology.
- Gallardo P., Murray R. and Krumdieck S. (2021) A sequential optimization-simulation approach for planning the transition to the low carbon freight system with case study in the North Island of New Zealand. Energies 14(11) http://dx.doi.org/10.3390/en14113339.
- Lam N., Murray R., Docherty PD., Te Morenga L. and Chase JG. (2021) The Effects of Additional Local-Mixing Compartments in the DISST Model-Based Assessment of Insulin Sensitivity. Journal of Diabetes Science and Technology http://dx.doi.org/10.1177/19322968211021602.
- Lam N., Docherty PD., Murray R., Chase JG. and Morenga LT. (2020) Using the Adapted Levenberg-Marquardt method to determine the validity of ignoring insulin and glucose data that is affected by mixing. IFAC-PapersOnLine 53(2): 16341-16346. http://dx.doi.org/10.1016/j.ifacol.2020.12.661.
- Laufer B., Murray R., Docherty PD., Krueger-Ziolek S., Hoeflinger F., Reindl L. and Moeller K. (2020) A Minimal Set of Sensors in a Smart-Shirt to Obtain Respiratory Parameters. IFAC-PapersOnLine 53(2): 16293-16298. http://dx.doi.org/10.1016/j.ifacol.2020.12.627.
- Poole M., Murray R., Davidson SM. and Docherty PD. (2019) The quadratic dimensional reduction method for parameter identification. Communications in Nonlinear Science and Numerical Simulation 73: 425-436. http://dx.doi.org/10.1016/j.cnsns.2019.03.001.