Rachel Nicks

Room B23 · School of Mathematical Sciences, University of Nottingham · NG7 2RD · UK

+44 (0)115 951 4958 · rachel.nicks@nottingham.ac.uk

I am an Assistant Professor in the School of Mathematical Sciences at the University of Nottingham. My research interests lie in the area of nonlinear dynamical systems, in particular the role of symmetry in predicting the patterns of behaviour which solutions to nonlinear dynamical systems may exhibit. My most recent research involves the application of nonlinear dynamics techniques to problems in Mathematical Neuroscience

Research

My research interests lie in the area of nonlinear dynamical systems, in particular pattern formation, coupled oscillators, symmetric bifurcation theory and applications in mathematical neuroscience. Follow the links below for more details:

Sensory induced visual hallucinations

Coupled oscillator networks



Pattern formation and neural fields on spherical domains

Modelling solid crystals with defects

PhD Students


Mustafa Sayli : Nonsmooth dynamical systems: from nodes to networks PhD 2021
Abigail Cocks : The Dynamics of Neural Fields and Applications to Vision PhD 2022
James Ross : Mathematical Neuroscience: From Neural Fields to Neuroimaging Yr 4
Reem Almarashi : Dynamics of mass in mass chains
 Yr 3
Robert Allen : Phase-isostable descriptions of coupled oscillator networks
 Yr 3
Matthew Fellows : Pattern formation in next generation neural field models
 Yr 2

Publications

R Nicks, R Allen and S Coombes 2024 Insights into oscillator network dynamics using a phase-isostable framework, Chaos, Vol 34, 013141
S Coombes, M Sayli, R Thul, R Nicks, M A Porter and Y M Lai 2024 Oscillatory networks: Insights from piecewise-linear modelling, SIAM Review, to appear
M Sayli, A C Skeldon, R Thul, R Nicks and S Coombes 2023 The two process model for sleep-wake regulation: A nonsmooth dynamics perspective, Physica D, Vol 44, 133595
Á Byrne, J Ross, R Nicks and S Coombes 2022 Mean-field models for EEG/MEG: from oscillations to waves, Brain Topography, Vol 35, 36-53
R Nicks, A Cocks, D Avitabile, A Johnston and S Coombes 2021 Understanding sensory induced hallucinations: From neural fields to amplitude equations, SIAM Journal on Applied Dynamical Systems, Vol 20(4), 1683-1714
J Ross, M Margetts, R Nicks, I Bojak, D Avitabile and S Coombes 2020 A brain-wave equation incorporating axo-dendritic connectivity, Physical Review E, Vol 101, 022411
R Nicks, L Chambon and S Coombes 2018 Clusters in nonsmooth oscillator networks, Physical Review E, Vol 97, 032213
S Visser, R Nicks, O Faugeras and S Coombes, 2017 Standing and travelling waves in a spherical brain model: the Nunez model revisited, Physica D, Vol 349, 27–45
P Ashwin, S Coombes and R Nicks 2016 Mathematical frameworks for oscillatory network dynamics in neuroscience, Journal of Mathematical Neuroscience, 6:2
R Nicks 2014 A classification of the symmetries of uniform discrete defective crystals, Journal of Elasticity, Vol 117, 189-211
R Nicks and G P Parry 2014 Group elastic symmetries common to continuum and discrete defective crystals, Journal of Elasticity, Vol 115, 131-156
R Nicks and G P Parry 2013 Geometrical issues in the continuum mechanics of defective solid crystals, Miskolc Mathematical Notes, Vol 14, 199-213
R Nicks and G P Parry 2012 On symmetries of crystals with defects related to a class of solvable groups (S2), Mathematical Methods in the Applied Sciences, Vol 35, 1741-1755
R Nicks and G P Parry 2012 On symmetries of crystals with defects related to a class of solvable groups (S1), Mathematics and Mechanics of Solids, Vol 17, 631-651
G P Parry and R Sigrist 2012 Reconciliation of local and global symmetries for a class of crystals with defects, Journal of Elasticity, Vol 107, 81-104
R Sigrist and P Matthews 2011 Symmetric spiral patterns on a sphere, SIAM Journal on Applied Dynamical Systems, Vol 10, 1177-1211
R Sigrist 2010 Hopf bifurcation with spherical symmetry, Nonlinearity, Vol 23, 3199-3225

Teaching

I currently teach the Autumn Semester of MATH2012 Modelling with Differential Equations. All resources can be found on the Moodle page

Curriculum Vitae

Employment

University of Nottingham

Assistant Professor
School of Mathematical Sciences
August 2016 - Present

University of Birmingham

Lecturer in Applied Mathematics
School of Mathematics
January 2013 - July 2016

University of Nottingham

Research Fellow
School of Mathematical Sciences

Research funded by EPSRC via the "Modelling continuous and discrete defective crystals" grant.

December 2009 - December 2012

Education

PhD Mathematics

University of Nottingham

Supervisors: Dr Paul Matthews and Dr Stephen Cox.

2010

MMath Mathematics

University of Warwick
2006