Research/Scholarly/Creative Works

• 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. (Journal Articles)

• 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 39(10): 2769-2792. http://dx.doi.org/10.1017/etds.2017.143. (Journal Articles)

• 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. (Journal Articles)

• Murray R. (2018) Random dynamical systems and transfer operator cycles. University of Otago: 2018 New Zealand Mathematics Colloquium, 3-6 Dec 2018. (Conference Contributions - Other)

• 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. (Journal Articles)

• 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. (Conference Contributions - Published)

• 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. (Journal Articles)

• 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. (Conference Contributions - Other)

• 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. (Conference Contributions - Other)

• 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. (Conference Contributions - Other)

• 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. (Conference Contributions - Other)

• 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. (Conference Contributions - Other)

• 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. (Conference Contributions - Other)

• 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. (Journal Articles)

• 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. (Journal Articles)

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

• 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. (Journal Articles)

• Murray R. (2015) Approximation of invariant measures: Ulam's method and beyond. Valparaiso, Chile: Chile-New Zealand Workshop on Dynamical Systems, 6-8 Jan 2015. (Conference Contributions - Other)

• 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. (Journal Articles)

• 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. (Journal Articles)

• 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. (Chapters)

• Bose C. and Murray R.. (2014) Chapter 5 Numerical Approximation of Conditionally Invariant Measures via Maximum Entropy. In ERGODIC THEORY, OPEN DYNAMICS, AND COHERENT STRUCTURES 70: 81-104. http://dx.doi.org/10.1007/978-1-4939-0419-8__5. (Conference Contributions - Published)

• 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. (Journal Articles)

• Godsoe W., Murray R. and Plank M. (2014) Information on biotic interactions improves transferability of distribution models. . (Journal Articles)

• Murray R. (2014) Ulam's method for open dynamical systems. UNSW, Sydney, Australia: Sydney Dynamics Group Seminar. (Oral Presentations)

• Murray R. (2014) Computation of ergodic objects in dynamical systems. Rotorua, New Zealand: Australia and New Zealand Industrial and Applied Mathematics Conference 2014 (ANZIAM), 2-6 Feb 2014. (Conference Contributions - Other)

• Murray R. (2014) Invariant measures and where to find them. Melbourne, Australia: Special session on Groups and Dynamics, 8th Australia-New Zealand Mathematics Convention, 8-12 Dec 2014. (Conference Contributions - 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]. (Other)

• 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. (Conference Contributions - Other)

• Bose C. and Murray R. (2013) Polynomial decay of correlations in the generalized baker's transformation. International Journal of Bifurcation and Chaos 23(8) 1350130 http://dx.doi.org/10.1142/S0218127413501307. (Journal Articles)

• Murray R. (2013) Set oriented features of MAXENT type algorithms. Dresden, Germany: 4th International Workshop on Set-Oriented Numerics (SON2013), 29 Sep-2 Oct 2013. (Conference Contributions - Other)

• 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. (Conference Contributions - Other)

• 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. (Conference Contributions - Other)

• Murray R. (2012) Numerical approximation of conditionally invariant measures. Banff, Canada: BIRS Workshop on Open Dynamical Systems: Ergodic Theory, Probabilistic Methods and Applications, 8-13 Apr 2012. (Conference Contributions - Other)

• Murray R. (2012) Set-wise methods for the invariant measure problem: Convergence? Sydney, Australia: International workshop on Set Oriented Numerics (SON2012), 3-6 Sep 2012. (Conference Contributions - Other)

• 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. (Reports)

• 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. (Journal Articles)

• Murray R. and Bose C. (2011) New Computational Methods for Open Dynamics. Snowbird, UT, USA: SIAM Conference on Applications of Dynamical Systems, 22-26 May 2011. (Conference Contributions - Other)

• Murray R. (2010) Polynomial decay of correlations. Dunedin, New Zealand: 2010 New Zealand Mathematical Society Colloquium, 7-9 Dec 2010. (Conference Contributions - Other)

• 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. (Journal Articles)

• Murray R. (2009) Convergence of Ulam's Method for Non-uniformly Expanding Maps. Snowbird, UT, USA: 2009 SIAM Conference on Applications of Dynamical Systems (DS09), 17-21 May 2009. (Conference Contributions - Other)

• Murray R. (2009) Ulam's method without a spectral gap. Sydney, Australia: 1st Pacific Rim Mathematical Association (PRIMA) Congress, 6-10 Jul 2009. (Conference Contributions - Other)

• Murray R. and Bose C. (2009) Convexity violation in a simple option pricing model. Auckland, New Zealand: New Zealand Mathematics Colloquium 2009, 8-10 Dec 2009. (Conference Contributions - Other)

• 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. (Journal Articles)

• 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. (Journal Articles)

• Murray R. (2007) Entropy methods in dynamical systems. Melbourne, Australia: AMSI-MASCOS 2007: Concepts of Entropy and Their Applications, 26 Nov-11 Dec 2007. (Conference Contributions - Other)

• Murray R. (2007) Ulam's Method for Invariant Measures with an Indifferent Fixed Point. Wellington, New Zealand: 1st Joint International Meeting between the American Mathematical Society and the New Zealand Mathematical Society (AMS-NZMS 2007), 12-15 Dec 2007. (Conference Contributions - Other)

• Murray R. and Bose C. (2007) Slow Decay of Correlations in the Generalized Baker's Map. Snowbird, UT, USA: SIAM Conference on Applications of Dynamical Systems (DS07), 28 May-1 Jun 2007. (Conference Contributions - Other)

• 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. (Journal Articles)

• Bose CJ. and Murray R. (2006) Minimum 'energy' approximations of invariant measures for nonsingular transformations. Discrete and Continuous Dynamical Systems 14(3): 597-615. http://dx.doi.org/10.3934/dcds.2006.14.597. (Journal Articles)

• 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. (Journal Articles)

• 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]. (Other)

• Murray R. (2006) Invariant measures, approximately invariant measures and convex optimization. Alberta, Canada: Measurable Dynamics: Theory and Applications, 5-10 Aug 2006. (Conference Contributions - Other)

• Murray R. (2005) Accurate computation of invariant densities. Snowbird, UT, USA: SIAM conference on applications of dynamical systems, 1 May 2005. (Conference Contributions - Other)

• Murray R. (2004) Adaptive approximation for probing chaotic dynamics. University of Otago, Dunedin, New Zealand: New Zealand Mathematics Colloquium, 1 Dec 2004. (Conference Contributions - Other)

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

• Murray R. (2002) Orbit statistics for maps with indifferent fixed points. Auckland, New Zealand: NZ Mathematics Colloquium, 1 Dec 2002. (Conference Contributions - Other)

• Bose C. and Murray R. (2001) The exact rate of approximation in Ulam's method. Discrete and Continuous Dynamical Systems 7(1): 219-235. http://dx.doi.org/10.3934/dcds.2001.7.219. (Journal Articles)

• Murray R. (2001) Approximating topological entropy in the logistic family. Massey University, Palmerston North, New Zealand: NZ Mathematics Colloquium, 1 Dec 2001. (Conference Contributions - Other)

• 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. (Journal Articles)

• 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. In : 223-232. (Conference Contributions - Published)

• Murray R. (2000) Dynamical zeta-functions by Ulam's method. University of Surrey: 2nd LMS workshop on Numerical methods and dynamical systems, 30 Jun 2000. (Conference Contributions - Other)

• Murray R. (2000) Ergodic theory and rigorous computation in dynamical systems. University of Surrey, Guildford, UK: Twentieth European Dynamics Days 2000, 1 Jun 2000. (Conference Contributions - Other)

• Santoboni G., Murray R. and Bishop S. (2000) Roundoff-induced phenomena and diffusion processes: the ``premature'' synchronisation of coupled maps. Physics Letters A 271 271(5-6): 358-367. http://dx.doi.org/10.1016/S0375-9601(00)00381-9. (Journal Articles)

• 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]. (Other)

• Murray R. (1999) Computational approaches to mixing rates in dynamical systems. University of Cantebury, Christchurch, New Zealand: New Zealand Mathematics Colloquium, 1 Jul 1999. (Conference Contributions - Other)

• Murray R. (1999) Matrix approaches to mixing rates. Snowbird, UT, USA: SIAM conference on applications of dynamical systems, 1 May 1999. (Conference Contributions - Other)

• Murray R. (1999) Stochastic stability and Ulam's method. Snowbird, UT, USA: SIAM conference on applications of dynamical systems, 1 May 1999. (Conference Contributions - Other)

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

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

• Murray R. (1997) Cone conditions and error bounds for Ulam´s method. Snowbird, UT, USA: SIAM conference on applications of dynamical systems, 1 May 1997. (Conference Contributions - Other)

• Murray R. (1997) Discrete approximation of invariant densities. United Kingdom. University of Cambridge. (Theses / Dissertations)

• Murray R.. (1997) Invariant measures and stochastic discretisations of dynamical systems. In. (Conference Contributions - Published)

• Murray R. (1996) Approximation and concrete error bounds for ACIM density approximation for C^{1+α} expanding mappings. Statistical Laboratory Research Report 1996-22. . (Discussion/Working Papers)

• Murray R. (1996) Error bounds for approximation of absolutely continuous invariant measures. TU Delft, Netherlands: One-day Workshop on Ergodic Theory, 21 Aug 1996. (Conference Contributions - Other)

• Murray R. (1996) Stochastic discretisation: approximating invariant measures by noisy dynamics. An essay submitted for consideration for the J T Knight Prizes. . (Other)

Editorial Work

• Journal of Computational Dynamics Associate Editor ( 2012 - 2020)

Review and Refereeing

• Atlantic Electronic Journal of Mathematics ( 2006 - 2020)
• Dynamical Systems ( 2006 - 2020)
• Ergodic Theory and Dynamical Systems ( 2006 - 2020)
• Journal of Physics A ( 2006 - 2020)
• Journal of Sound and Vibration ( 2006 - 2020)
• New Zealand Journal of Mathematics ( 2006 - 2020)
• Nonlinearity ( 2006 - 2020)
• Physica Scripta ( 2006 - 2020)

Research Groups