Research/Scholarly/Creative Works

Journal Articles

• 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.

• Froyland G., Gonzalez-Tokman C. and Murray RDA. (2018) Quenched stochastic stability for eventually expanding-on-average random interval map cocycles. Ergodic Theory and Dynamical Systems : 24. http://dx.doi.org/10.1017/etds.2017.143.

• 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.

• 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.

• Mohd MH., Murray R., Plank MJ. and Godsoe W. (2016) Effects of dispersal and stochasticity on the presence–absence of multiple species. Ecological Modelling 342: 49-59. http://dx.doi.org/10.1016/j.ecolmodel.2016.09.026.

• Godsoe W., Murray R. and Plank MJ. (2015) Information on biotic interactions improves transferability of distribution models. The American naturalist 185(2): 281-290. http://dx.doi.org/10.1086/679440.

• Godsoe W., Murray R. and Plank MJ. (2015) The effect of competition on species' distributions depends on coexistence, rather than scale alone. Ecography 38(11): 1071-1079. http://dx.doi.org/10.1111/ecog.01134.

• Bose C. and Murray R. (2014) First hyperbolic times for intermittent maps with unbounded derivative. Dynamical Systems: An International Journal 29(3): 352-368. http://dx.doi.org/10.1080/14689367.2014.902038.

• Bose C. and Murray R. (2014) Maximum Entropy Estimates for Risk-Neutral Probability Measures with Non-Strictly-Convex Data. Journal of Optimisation Theory and Applications 161(1): 285-307. http://dx.doi.org/10.1007/s10957-013-0349-x.

• Bose C., Froyland G., González-Tokman C. and Murray R. (2014) Ulam's Method for Lasota-Yorke Maps with Holes. SIAM Journal on Applied Dynamical Systems 13(2): 1010-1032. http://dx.doi.org/10.1137/130917533.

• BOSE CHRISTOPHER. and MURRAY RUA. (2013) Polynomial decay of correlations in the generalized baker's transformation. International Journal of Bifurcation and Chaos 23(08): 1350130-1350130. http://dx.doi.org/10.1142/s0218127413501307.

• Froyland G., Murray R. and Stancevic O. (2011) Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity 24: 2435-2463. http://dx.doi.org/10.1088/0951-7715/24/9/003.

• Murray R. (2010) Ulam's method for some non-uniformly expanding maps. Discrete and Continuous Dynamical Systems 26(3): 1007-1018. http://dx.doi.org/10.3934/dcds.2010.26.1007.

• Bose CJ. and Murray R. (2007) Duality and the Computation of Approximate Invariant Densities for Nonsingular Transformations. SIAM Journal on Optimization 18(2): 691-709. http://dx.doi.org/10.1137/060658163.

• Froyland G., Murray R. and Terhesiu D. (2007) Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 76(3): 36702. http://dx.doi.org/10.1103/PhysRevE.76.036702.

• Bose CJ. and Murray R. (2006) Dynamical conditions for convergence of a maximum entropy method for Frobenius-Perron operator equations. Applied Mathematics and Computation 182(1): 210-212. http://dx.doi.org/10.1016/j.amc.2006.01.089.

• Bose CJ. and Murray R. (2006) Minimum 'energy' approximations of invariant measures for nonsingular transformations. Discrete and Continuous Dynamical Systems 14(3): 597-615.

• Domijan M., Murray R. and Sneyd J. (2006) Dynamical Probing of the Mechanisms Underlying Calcium Oscillations. Journal of Nonlinear Science 16(5): 483-506. http://dx.doi.org/10.1007/s00332-005-0744-z.

• Murray R. (2004) Optimal partition choice for invariant measure approximation for one-dimensional maps. Nonlinearity 17(5): 1623-1644. http://dx.doi.org/10.1088/0951-7715/17/5/004.

• Bose C. and Murray R. (2001) The exact rate of approximation in Ulam's method. Discrete and Continuous Dynamical Systems 7(1): 219-235.

• Murray R. (2001) Existence, mixing and approximation of invariant densities for expanding maps on R^r. Nonlinear Analysis: Theory, Methods and Applications 45(1): 37-72. http://dx.doi.org/10.1016/S0362-546X(99)00329-6.

• Santoboni G., Murray R. and Bishop SR. (2000) Roundoff-induced phenomena and diffusion processes: the ``premature'' synchronisation of coupled maps. Physics Letters A 271(5-6): 358-367. http://dx.doi.org/10.1016/s0375-9601(00)00381-9.

• Keane M., Murray R. and Young L-S. (1998) Computing invariant measures for expanding circle maps. Nonlinearity 11(1): 27-46. http://dx.doi.org/10.1088/0951-7715/11/1/004.

• Murray R. (1998) Approximation error for invariant density calculations. Discrete and Continuous Dynamical Systems 4(3): 535-557. http://dx.doi.org/10.3934/dcds.1998.4.535.

Chapters

• Bose C. and Murray R. (2014) Numerical approximation of conditionally invariant measures via Maximum Entropy. In Bahsoun W; Bose C; Froyland G (Ed.), Ergodic theory, open dynamics, and coherent structures. Springer Proceedings in Mathematics & Statistics, Vol 70: 81-104. New York: Springer-Verlag. http://dx.doi.org/10.1007/978-1-4939-0419-8_5.

Conference Contributions - Published

• 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. In IFAC-PapersOnLine 50(1): 5474-5479. http://dx.doi.org/10.1016/j.ifacol.2017.08.1085.

• Santoboni G., Murray R. and Bishop S. (2001) A simple use of the diffusion approximation for treating roundoff-induced problems in coupled maps with an invariant subset. Pamplona, Spain: Space-time chaos, 1 Jan 2000. : 223-232.

• Murray R. (1997) Invariant measures and stochastic discretisations of dynamical systems. Berlin Germany: 15th IMACS World Congress on Scientific Computation, 1 Aug 1997.

Conference Contributions - Other

• Fee CJ., Newberry F., Gordon A., Wilson P., Moyers-Gonzales M., Murray R., Huber T. and Dimartino S. (2016) Optimization of porous bed geometric features to maximize adsorption of proteins and passage of suspended solids in a 3D-printed adsorption column. Philadelphia, PA, USA: PREP Symposium 2016, 18-21 Jul 2016.

• Fee CJ., Newberry F., Gordon A., Wilson PL., Moyers-Gonzalez M., Murray R., Huber T. and Dimartino S. (2016) 3D-printed chromatography columns for downstream capture of proteins in the presence of suspended cells. Phuket, Thailand: 2nd Bioprocess Asia Conference, 5-8 Dec 2016.

• Froyland G., De Jong J., Moyers-Gonzales M., Roberts B., Wilson PL. and Murray R. (2016) Vortices in a street canyon. Orlando, FL, USA: The 11th AIMS Conference on Dynamical Systems, Differential Equations and Applications, 1-5 Jul 2016.

• Goodman M., David T., Docherty PD. and Murray R. (2016) Calcium Dynamics in Coupled Cellular Reaction Diffusion Equations. Queenstown, New Zealand: 34th Australasian Winter Conference on Brain Research, 27-31 Aug 2016.

• Goodman M., David T., Docherty PD. and Murray R. (2016) Homogenisation Theory Applied to Coupled Mammalian Cells. Christchurch, New Zealand: Health Research Society of Canterbury: Christchurch Hospitals' Grand Rounds series 2016, 27-27 May 2016.

• Goodman M., Murray R., Docherty PD. and David T. (2016) Homogenisation Theory with Coupled Cellular Reaction Diffusion Equations. Boston, MA, USA: SIAM Conference on the Life Sciences 2016, 11-14 Jul 2016.

• Asuncion J., Krumdieck S., Rendall S., Page S. and Murray R. (2013) Geographic Energy Adaptive Potential of Farmers' Market System as Compared with Conventional Supermarket System. Washington DC, USA: Transportation Research Board 92nd Annual Meeting, 13-17 Jan 2013.

• Asuncion J., Page S., Murray R. and Krumdieck S. (2012) Analysis of the truck trip generation characteristics of supermarkets and convenience stores. Rotorua, New Zealand: IPENZ Transportation Group Conference, 18-21 Mar 2012.

• Asuncion J., Rendall S., Murray R. and Krumdieck S. (2012) New Zealand intermodal freight network and the potential for mode shifting. Rotorua, New Zealand: IPENZ Transportation Group Conference, 18-21 Mar 2012.

Reports

• Bose C., Froyland G., Gonzalez-Tokman C. and Murray R. (2011) New methods for analysing metastable structures in closed, open or non-autonomous dynamical systems.Commissioned by Banff International Research Station. 5pp.

Other

• Ackerley E. and Murray R. (2013) Progress on Improving Student Success in First-Year Mathematics at the University of Canterbury. The CULMS Newsletter 8: 7-10. [Print and Online].

• Murray R. (2006) Geon Ho Choe, Computational Ergodic Theory. Algorithms and Computation in Mathematics 13, 2005; 453pp. Newsletter of the New Zealand Mathematical Society 96: 28-29. Wellington: New Zealand Mathematical Society Inc.. [Book Review].

• Murray R. (1999) Book review: "B Kitchens. Symbolic dynamics: one-sided, two-sided and countable state Markov shifts, Springer-Verlag (1998).". UK Nonlinear News 16 [Electronic].

Student Supervision

Displaying all items.

Current
• PhD - Gallardo PO: Essential elements of the energy transition for freight movements in post-colonial countries: data mining, modelling tools and policy scenarios - with case study in Ecuador (2020)
Completed
• PhD - Asuncion J: The geographic adaptive potential of freight transportation and production system in the context of fuel and emission constraints (2013)
• PhD - Mohd M: Modelling the Presence-Absence of Multiple Species (2016)
• Masters - Litchfield B: Implementation of chaos based communication systems in real time (2017)
• Masters - Shek J: Homogenised models of smooth muscle and endothelial cells (2013)
• Masters - Sung J: Reconstructing distributions from option prices (2013)
• Honours - Di S: Metastability in open dynamical systems (2013)
• Honours - Fisher K: Excitability in Random Dynamical Systems (2017)
• Honours - Kempe A: Bank failure in complex financial networks (2013)
• Honours - Mugford J: Coupled cell dynamics (2013)
• Honours - Williams J: L^2 quantization of area preserving maps (2011)
• Summer Student - Churcher K: Large-scale networks of nonlinear oscillators: parameter gradients, spatio-temporal decoherence and chaos. (2012)
• Summer Student - Newberry F: Geometry optimisation of porous media (2016)
• Summer Student - Roberts B: Coherent Structures in High Reynolds Number Flows (2016)

Research Groups