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.
- Mohd MH., Murray R., Plank MJ. and Godsoe W. (2018) Effects of different dispersal patterns on the presence-absence of multiple species. Communications in Nonlinear Science and Numerical Simulation 56: 115-130. http://dx.doi.org/10.1016/j.cnsns.2017.07.029.
- Davidson SM., Docherty PD. and Murray R. (2017) The dimensional reduction method for identification of parameters that trade-off due to similar model roles. Mathematical Biosciences 285: 119-127. http://dx.doi.org/10.1016/j.mbs.2017.01.003.
- Davidson SM., Docherty PD., Kretschmer J. and Murray R. (2017) The Novel Dimensional Reduction Method and Tikhonov Regularisation in Parameter Identification of Non-Linear Ill-Posed Problems. IFAC-PapersOnLine 50(1): 5474-5479. http://dx.doi.org/10.1016/j.ifacol.2017.08.1085.
- Mohd MH., Murray R., Plank MJ. and Godsoe W. (2017) Effects of biotic interactions and dispersal on the presence-absence of multiple species. Chaos, Solitons and Fractals 99: 185-194. http://dx.doi.org/10.1016/j.chaos.2017.04.012.
- Gray RAL., Docherty PD., Fisk LM. and Murray R. (2016) A modified approach to objective surface generation within the Gauss-Newton parameter identification to ignore outlier data points. Biomedical Signal Processing and Control 30: 162-169. http://dx.doi.org/10.1016/j.bspc.2016.06.009.