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Jonathan Crofts

Senior Lecturer

Physics and Mathematics

Staff Group(s)
Physics and Mathematics


Dr Jonathan Crofts is a Senior Lecturer of Applied Mathematics. His teaching currently includes the modules Advanced Calculus (Year 2), Linear Systems (Year 3) and Topics in Mathematical Biology (Year 4). His research is primarily concerned with the modelling of complex biological systems using the techniques of network science, and applied mathematics more generally.

Career overview

Dr  Crofts completed his PhD at the University of Leicester in 2007. His research centred around the development of novel numerical schemes to detect unstable periodic orbits (UPOs) in both continuous and discrete dynamical systems. This work provided a first rigorous mathematical analysis of the so-called stabilising transformation technique for determining UPOs, and, as a result, the application of this method to very high (possibly infinite) dimensional systems.

Dr Crofts then moved to the University of Strathclyde to work on the MRC funded project Complex Brain Networks in Health Development and Disease. As part of the project he spent an initial 6 months at the University of Oxford being trained in computational neuroscience/imaging. This included attendance at MSc level neuroscience lectures, as well as training in fundamental neuroimaging techniques and software packages such as FSL, Freesurfer and Caret. Working closely with neuroscientists at Oxford, he developed a number of mathematical computational tools for analysing brain anatomical networks arising in neuroinformatics.

In 2010, Dr Crofts joined Nottingham Trent University as a lecturer in Applied Mathematics. In 2015 Dr Crofts was promoted to his present Senior Lecturer role.

Research areas

Dr Crofts is a member of the Biomathematics and Bioinformatics research group.

His research interests are in computational and applied mathematics with strong interests in computational biology including:

  • Mathematics of networks, hypernetworks and multiplex networks
  • Dynamical systems on networks
  • Applications of networks to biology
  • Understanding structure-function relations in biological networks
  • Network classification problems

If you are considering applying for an MRes or PhD in any of the areas above, please email Dr Crofts for further information. Some available PhD titles include:

  • Multiplex network models of the brain
  • Dynamics on spatially constrained brain networks
  • A multiplex network approach to cancer patient stratification and identification of subtype-specific prognostic multi-omics signatures

Opportunities arise to carry out postgraduate research towards an MPhil / PhD in the areas identified above. Further information may be obtained on the NTU Research Degrees website

Current and recent postgraduate supervisory experience:

Research fellows:

  • Casimiro Pio Carrino Investigating the role of non-reciprocal prefrontal connectivity in attentional processing: a computational approach (2016)
  • Dr Yi-Ping Lo Simulation and analysis of epileptic seizure progression (2012-2013)

PhD Students

  • Iain Pinder (in progress) Dynamics on spatially constrained complex brain networks
  • Suliman Almansour (in progress) Mathematical modelling of macrophage phenotype selection: its role in inflammation and tissue repair
  • Amelia Padmore (in progress) Modelling the impact of structural directionality on large-scale models of neural activity
  • Jacob Rowbottom (in progress) A hybrid convolution quadrature method for modelling time-dependent waves with broadband frequency content
  • Michael Forrester (completed 2020) Modelling of large-scale brain network dynamics
  • Anahita Bayani (completed 2020) Spatial considerations in the resolution of inflammation
  • Bethany Hall (completed 2020) In silico modelling of longevity of Drosophila melanogaster: a network approach
  • Rebecca Martin (completed 2018) Collocation techniques for solving neural field models on complex cortical geometries
  • Daniel Buxton (completed 2017) Remotely acting mutations in genetic disease and cancer: features and properties
  • Nicole Pearcy (completed 2015) Unravelling the complexity of metabolic networks
  • Stacey Bedwell (completed 2015) Topographic connectivity of the mammalian prefrontal cortex

MRes students

  • Iain Pinder (completed 2019) Synchrony and bifurcations in a network of delayed Wilson-Cowan oscillators

External activity

  • Refereeing for scientific journals:
    • Journal of Complex Networks
    • Chaos
    • PLOS Computational Biology
    • PLOS ONE
    • Scientific Reports
    • Europhysics Letters
    • Physica A
    • Cerebral Cortex
    • Network Neuroscience
    • Proceedings of the Royal Society A Mathematical, Physical and Engineering Sciences

Sponsors and collaborators

Current and recent research is being conducted in collaboration with:

  • Reuben O'Dea, University of Nottingham
  • Marcus Kaiser, University of Nottingham
  • Stephen Coombes, University of Nottingham
  • Yvonne Barnett, Anglia Ruskin University
  • Cheol E Han, Korea University
  • Des Higham, University of Strathclyde
  • Ernesto Estrada, University of  Zaragoza
  • Ruslan Davidchack, University of  Leicester



Bayani, A., Dunster, J.L., Crofts, J.J. and Nelson, M.R. 2020. Spatial considerations in the resolution of inflammation: Elucidating leukocyte interactions via an experimentally calibrated agent-based model PLoS Computational Biology, 16(11):e1008413. ISSN 1553-7358

Padmore, A., Nelson, M.R., Chuzhanova, N. and Crofts, J.J. 2020. Modelling the impact of structural directionality on connectome-based models of neural activity Journal of Complex Networks, 8(4):cnaa033. ISSN 2051-1329

Forrester, M., Crofts, J.J., Sotiropoulos,  S.N., Coombes, S. and O'Dea, R.D., 2020. The role of node dynamics in shaping the emergent functional connectivity patterns in the brain Network Neuroscience, 4(2):467-483. ISSN 2472-1751

Bayani, A., Dunster, J.L., Crofts, J.J. and Nelson, M.R., 2020. Mechanisms and points of control in the spread of inflammation: A mathematical investigation Bulletin of Mathematical Biology, 82(4). ISSN 0092-8240

Hall. B., Barnett. Y., Crofts, J.J. and Chuzhanova, N., 2019. Identification of novel genes associated with longevity in Drosophila melanogaster - a computational approach Aging, 2019, 11:1-24. ISSN 1945-4589

Buxton, D.S., Batten, D.J., Crofts, J.J. and Chuzhanova, N., 2019. Predicting novel genomic regions linked to genetic disorders using GWAS data and 3D architecture of the human genome - a case study of schizophrenia Scientific Reports, 9:17940. ISSN 2045-2322

Martin, R., Chappell, D.J., Chuzhanova, N. and Crofts, J.J., 2018. A numerical simulation of neural fields on curved geometries Journal of Computational Neuroscience, 45(6):859-873. ISSN 0929-5313

Crofts, J.J., Forrester, M. and O'Dea, R.D., 2016. Structure-function clustering in multiplex brain networks Europhysics Letters, 116(1):18003. ISSN 0295-5075

Pearcy, N., Chuzhanova, N. and Crofts, J.J., 2016. Complexity and robustness in hypernetwork models of metabolism Journal of Theoretical Biology, 406:99-104. ISSN 0022-5193

Lo, Y.P., O'Dea, R.D., Crofts, J.J., Han, C.E. and Kaiser, M., 2015. A geometric network model of intrinsic grey-matter connectivity of the human brain Scientific Reports, 5:15397. ISSN 2045-2322

See all of Jonathan Crofts's publications...