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Dr. Gavin Abernethy PhD, MMath

Lecturer in Engineering Mathematics


Summary

I joined Sheffield Hallam University in 2018 after completing my PhD at Ulster University. I primarily teach mathematical techniques to students on engineering courses, and conduct research in mathematical modelling. In particular, I am interested in simulating population dynamics upon complex adaptive networks.

About

I studied mathematics at the University of St Andrews, where I developed an interest in real and abstract analysis, fractal geometry and chaos and dynamical systems. Returning to Northern Ireland, I undertook a PhD in the artificial intelligence research group at Ulster University on mathematical models of evolutionary food web development. This mainly consisted of developing population models and programming large-scale numerical simulations in Fortran 90. Following completion of this, I joined Sheffield Hallam University in August 2018. In my present post, my main responsibility is teaching applied mathematical techniques to engineering students, such as the use of differential equations, matrix methods, and Fourier series. I am continuing research on ecological models with spatial and evolutionary elements, and have recently developed an interest in applying similar techniques to epidemiological contexts. Occasionally, I also publish pedagogical discussions of undergraduate population modelling projects.

Teaching

Department of Engineering and Mathematics

Business, Technology and Enterprise

Subject Area

Physics and Engineering Mathematics.

Modules

Maths for Materials and Design; Railway Engineering Mathematics for Apprentices.

Research

My current interests are concerned with simulating different kinds of population dynamics superimposed upon complex adaptive networks. These include: - Eco-evolutionary models of the co-evolution of species populations in spatial networks, and the applications of these models to conservation science. - Epidemiological models structured by space and age, to help us understand the spread of infectious diseases during a pandemic and seek optimal management strategies. - Models of ideological dynamics in social groups.

Publications

Journal articles

Abernethy, G. (2021). Sequences of patch disturbance in a spatial eco-evolutionary model. Communications in Nonlinear Science and Numerical Simulation, 97, 105746. http://doi.org/10.1016/j.cnsns.2021.105746

Abernethy, G. (2020). A model of invasion by bodysnatchers from the far reaches of space. International Journal of Mathematical Education in Science and Technology. http://doi.org/10.1080/0020739X.2020.1850896

Abernethy, G. (2020). Allometry in an eco-evolutionary network model. Ecological Modelling, 427, 109090. http://doi.org/10.1016/j.ecolmodel.2020.109090

Abernethy, G., McCartney, M., & Glass, D.H. (2019). The robustness, link-species relationship and network properties of model food webs. Communications in Nonlinear Science and Numerical Simulation, 70, 20-47. http://doi.org/10.1016/j.cnsns.2018.09.002

Abernethy, G., McCartney, M., & Glass, D.H. (2019). The role of migration in a spatial extension of the Webworld eco-evolutionary model. Ecological Modelling, 397. http://doi.org/10.1016/j.ecolmodel.2018.12.003

Abernethy, G. (2018). Zombies: a simple discrete model of the apocalypse. International journal of mathematical education in science and technology, 49 (8), 1260-1277. http://doi.org/10.1080/0020739X.2018.1455229

Abernethy, G., McCartney, M., & Glass, D.H. (2018). The interaction between predator strategy and prey competition in a pair of multi-predator multi-prey lattices. Communications in nonlinear science and numerical simulation, 56, 9-33. http://doi.org/10.1016/j.cnsns.2017.06.012

Abernethy, G.M., & McCartney, M. (2017). Cannibalism and chaos in the classroom. International Journal of Mathematical Education in Science and Technology, 48 (1), 117-129. http://doi.org/10.1080/0020739X.2016.1184337

Abernethy, G.M., Mullan, R., Glass, D.H., & McCartney, M. (2017). A multiple phenotype predator–prey model with mutation. Physica A: Statistical Mechanics and its Applications, 465, 762-774. http://doi.org/10.1016/j.physa.2016.08.037

Mullan, R., Abernethy, G.M., Glass, D.H., & McCartney, M. (2016). A single predator multiple prey model with prey mutation. Communications in Nonlinear Science and Numerical Simulation, 40, 51-70. http://doi.org/10.1016/j.cnsns.2016.04.013

Abernethy, G.M., & McCartney, M. (2016). Analysis of a class of low-dimensional models of mutation and predation. International Journal of Bifurcation and Chaos, 26 (11). http://doi.org/10.1142/S0218127416300299

McCartney, M., Abernethy, G., & Gault, L. (2010). The divider dimensions of the irish coast. Irish Geography, 43 (3), 277-284. http://doi.org/10.1080/00750778.2011.582632

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