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Prof Alastair M Rucklidge

Head of School of Mathematics
Professor of Applied Mathematics
Applied Mathematics

Contact details

Room: 9.04
Tel: +44 (0)113 3435161
Email: A.M.Rucklidge @


Pattern formation
Mode interactions
Spatio-temporal chaos
Nonlinear and chaotic dynamics
Heteroclinic networks
Dynamo theory

Research interests

Regular patterns are ubiquitous in nature, and their formation and stability is governed by the intricate interactions of symmetry and nonlinearity. My research aims to understand how the nonlinear interaction of waves in different directions leads to the formation of (for example) quasipatterns (one of the outstanding problems of pattern formation), spatio-temporal chaos and other forms of chaotic dynamics. My work ranges from quantitative explanations of fluid dynamics experiments and large-scale numerical solutions of the equations for convection with magnetic fields, through developing new models for understanding mode interactions, to new ideas on heteroclinic networks, and existence proofs for quasipatterns.

Useful links

Personal research web page
Link to papers on
Link to ResearcherID
Link to ResearchGate

Current postgraduate students

Haifaa Alrihieli (2016)
Andrzej Kucik (2013)
Andrew Mellor (2013)


Rucklidge AM, Postlethwaite CM Spirals and heteroclinic cycles in a spatially extended Rock-Paper-Scissors model of cyclic dominance EPL, 117, 2017
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Rucklidge AM, Knobloch E Chaos in the Takens–Bogdanov bifurcation with O(2) symmetry Dynamical Systems, 1-20, 2016
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Mobilia M, Rucklidge AM, Szczesny B The influence of mobility rate on spiralwaves in spatial rock-paper-scissors games Games, 7, 2016
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Subramanian P, Archer AJ, Knobloch E, Rucklidge AM Three-Dimensional Icosahedral Phase Field Quasicrystal Physical Review Letters, 117, 2016
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Subramanian P; Archer AJ; Knobloch E; Rucklidge A Data associated with’Three-dimensional Icosahedral Phase Field Quasicrystal’ 2016

Archer AJ, Rucklidge AM, Knobloch E Soft-core particles freezing to form a quasicrystal and a crystal-liquid phase Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 92, 2015
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Skeldon AC, Rucklidge AM Can weakly nonlinear theory explain Faraday wave patterns near onset? Journal of Fluid Mechanics, 777, 604-632, 2015
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Mellor A, Mobilia M, Redner S, Rucklidge AM, Ward JA Influence of Luddism on innovation diffusion Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 92, 2015
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Szolnoki A, Mobilia M, Jiang LL, Szczesny B, Rucklidge AM, Perc M Cyclic dominance in evolutionary games: A review Journal of the Royal Society Interface, 11, 2014
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Szczesny B, Mobilia M, Rucklidge AM Characterization of spiraling patterns in spatial rock-paper-scissors games Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 90, 2014
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Bale CSE, McCullen NJ, Foxon TJ, Rucklidge AB, Gale WF Modeling diffusion of energy innovations on a heterogeneous social network and approaches to integration of real-world data Complexity, 19, 83-94, 2014
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Alnahdi AS, Niesen J, Rucklidge AM Localized patterns in periodically forced systems SIAM Journal on Applied Dynamical Systems, 13, 1311-1327, 2014
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Bale CSE, Gale WF, McCullen NJ, Rucklidge AM, Foxon TJ Harnessing social networks for promoting adoption of energy technologies in the domestic sector Energy Policy, 63, 833-844, 2013
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Archer AJ, Rucklidge AM, Knobloch E Quasicrystalline order and a crystal-liquid state in a soft-core fluid. Physical review letters, 111, 165501, 2013
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McCullen NJ, Rucklidge AM, Bale CSE, Foxon TJ, Gale WF Multiparameter Models of Innovation Diffusion on Complex Networks SIAM Journal on Applied Dynamical Systems, 12, 515-532, 2013
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Botha GJJ, Rucklidge AM, Hurlburt NE Formation of magnetic flux tubes in cylindrical wedge geometry Geophysical and Astrophysical Fluid Dynamics, 106, 701-709, 2012
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Szczesny B, Mobilia M, Rucklidge AM When does cyclic dominance lead to stable spiral waves? Europhysics Letters: a letters journal exploring the frontiers of physics, 102, 2012
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Kirk V, Postlethwaite C, Rucklidge AM Resonance bifurcations of robust heteroclinic networks SIAM Journal on Applied Dynamical Systems, 11, 1360-1401, 2012
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Bale CSE; McCullen, NJ; Foxon, TJ; Rucklidge AM; Gale WF Modelling diffusion of energy efficiency measures on a social network: Integration of real world dataEPSRC Complexity Science in the Real World Network - Academic Conference 2012

Bale C; McCullen N; Foxon T; Rucklidge A; Gale WF Local authority interventions in the domestic sector and the role of social networks : a case study from the city of LeedsEnergy and People: Futures, complexity and challenges 2012

Rucklidge AM, Silber M, Skeldon AC Three-wave interactions and spatiotemporal chaos Physical Review Letters, 108, 2012
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Weliwita JA, Rucklidge AM, Tobias SM Skew-varicose instability in two-dimensional generalized Swift-Hohenberg equations PHYS REV E, 84, 2011


Iooss G, Rucklidge AM On the Existence of Quasipattern Solutions of the Swift-Hohenberg Equation J NONLINEAR SCI, 20, 361-394, 2010

Kirk V, Lane E, Postlethwaite CM, Rucklidge AM, Silber M A mechanism for switching near a heteroclinic network DYNAM SYST, 25, 323-349, 2010

Rucklidge AM, Silber M Design of Parametrically Forced Patterns and Quasipatterns SIAM J APPL DYN SYST, 8, 298-347, 2009

Botha GJJ, Busse FH, Hurlburt NE, Rucklidge AM Numerical simulations of rotating axisymmetric sunspots MON NOT R ASTRON SOC, 387, 1445-1462, 2008

Kirk V, Rucklidge AM The effect of symmetry breaking on the dynamics near a structurally stable heteroclinic cycle between equilibria and a periodic orbit DYNAM SYST, 23, 43-74, 2008

Botha GJJ, Rucklidge AM, Hurlburt NE Nonaxisymmetric instabilities of convection around magnetic flux tubes ASTROPHYS J, 662, L27-L30, 2007

Rucklidge AM, Silber M Quasipatterns in parametrically forced systems PHYS REV E, 75, 2007

Botha GJJ; Rucklidge AM; Hurlburt NE Numerical simulations of sunspotsProceedings of the International Astronomical Union, 507-509 2006
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Botha GJJ, Rucklidge AM, Hurlburt NE Converging and diverging convection around axisymmetric magnetic flux tubes MON NOT R ASTRON SOC, 369, 1611-1624, 2006

Botha GJJ, Rucklidge AM, Busse FH, Hurlburt NE Numerical simulations of rotating sunspots European Space Agency, (Special Publication) ESA SP, 2006
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Rucklidge AM, Proctor MRE, Prat J Mean flow instabilities of two-dimensional convection in strong magnetic fields GEOPHYS ASTRO FLUID, 100, 121-137, 2006

Ashwin P, Rucklidge AM, Sturman R Cycling chaotic attractors in two models for dynamics with invariant subspaces CHAOS, 14, 571-582, 2004

Ashwin P, Rucklidge AM, Sturman R Two-state intermittency near a symmetric interaction of saddle-node and Hopf bifurcations: a case study from dynamo theory PHYSICA D, 194, 30-48, 2004

Rucklidge AM, Champneys AR Boundary effects and the onset of Taylor vortices PHYSICA D, 191, 282-296, 2004

Rucklidge AM Convergence properties of Fourier mode representations of quasipatterns In Dynamics and Bifurcation of Patterns in Dissipative Systems, 124-139, 2004
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Rucklidge AM Pattern formation in large domains PHILOS T ROY SOC A, 361, 2649-2664, 2003

Ashwin P, Field M, Rucklidge AM, Sturman R Phase resetting effects for robust cycles between chaotic sets CHAOS, 13, 973-981, 2003

Rucklidge AM, Rucklidge WJ Convergence properties of the 8, 10 and 12 mode representations of quasipatterns PHYSICA D, 178, 62-82, 2003

Dawes JHP, Matthews PC, Rucklidge AM Reducible actions of D-4 X T-2: superlattice patterns and hidden symmetries NONLINEARITY, 16, 615-645, 2003

Ashwin P; Rucklidge AM; Sturman R Cycling attractors of coupled cell systems and dynamics with symmetry. In:Pikovsky A; Maistrenko Y eds. 109, 5-23 2003

Rucklidge AM; Silber M; Fineberg J Secondary instabilities of hexagons: A bifurcation analysis of experimentally observed Faraday wave patterns. In:Buescu J; Castro S; Dias AP; Labouriau I eds. 101-114 2003

Hurlburt NE, Alexander D, Rucklidge AM Complete models of axisymmetric sunspots: Magnetoconvection with coronal heating ASTROPHYS J, 577, 993-1005, 2002

Ashwin P, Rucklidge AM, Sturman R Infinities of stable periodic orbits in systems of coupled oscillators PHYS REV E, 66, 2002

Rucklidge AM Global bifurcations in the Takens-Bogdanov normal form with D-4 symmetry near the O(2) limit PHYS LETT A, 284, 99-111, 2001

Melbourne I; Proctor MRE; Rucklidge AM A heteroclinic model of geodynamo reversals and excursions. 26, 363-370 2001
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Weiss NO, Rucklidge AM, Proctor MRE, Matthews PC, Brownjohn DP Numerical studies of pattern formation in three-dimensional magnetoconvection Progress of Theoretical Physics Supplement, 674-683, 2000
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Tse DP, Rucklidge AM, Hoyle RB, Silber M Spatial period-multiplying instabilities of hexagonal Faraday waves Physica D: Nonlinear Phenomena, 146, 367-387, 2000
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Rucklidge AM, Weiss NO, Brownjohn DP, Matthews PC, Proctor MRE Compressible Magnetoconvection in Three Dimensions: Pattern Formation in a Strongly Stratified Layer Journal of Fluid Mechanics, 419, 283-323, 2000
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Hurlburt NE, Rucklidge AM Development of Structure in Pores and Sunspots: Flows Around Axisymmetric Magnetic Flux Tubes Monthly Notices of the Royal Astronomical Society., 314, 793-806, 2000
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Hurlbert NE, Matthews PC, Rucklidge AM Solar magnetconvection Solar Physics, 192, 109-118, 2000
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Gog J, Oprea I, Proctor M, Rucklidge A Destabilization by noise of transverse perturbations to heteroclinic cycles: a simple model and an example from dynamo theory Proc Roy Soc Lond A, 455, 4205-4222, 1999
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Blanchflower SM, Rucklidge AM, Weiss NO Modelling photospheric magnetoconvection Monthly Notices of the Royal Astronomical Society, 301, 593-608, 1998
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Ashwin P, Rucklidge AM Cycling Chaos: Its Creation, Persistence and Loss of Stability in a Model of Nonlinear Magnetoconvection Physica D: Nonlinear Phenomena, 122, 134-154, 1998
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Rucklidge AM, Silber M Bifurcations of Periodic Orbits with Spatio-Temporal Symmetries Nonlinearity, 11, 1435-1455, 1998
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Rucklidge AM, Silber M Instabilities of periodic orbits with spatio-temporal symmetries Nonlinearity, 11, 1435-1455, 1997
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Rucklidge AM, Matthews PC Analysis of the shearing instability in nonlinear convection and magnetoconvection Nonlinearity, 9, 311-351, 1996
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Matthews PC, Rucklidge AM, Weiss NO, Proctor MRE The three-dimensional development of the shearing instability of convection Physics of Fluids, 8, 1350-1352, 1996
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Knobloch E, Proctor MRE, Rucklidge AM, Weiss NO Comment on‘‘Bifurcations from periodic solution in a simplified model of two‐dimensional magnetoconvection,’’ by N. Bekki and T. Karakisawa [Phys. Plasmas 2 , 2945 (1995)] Physics of Plasmas, 3, 2475-2476, 1996

Rucklidge AM Symmetry-breaking instabilities of convection in squares Proceedings of the Royal Society A: Mathematical, Physical&Engineering Science, 453, 107-118, 1996
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Rucklidge AM Chaos in magnetoconvection Nonlinearity, 7, 1565-1591, 1994
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Matthews PC, Proctor MRE, Rucklidge AM, Weiss NO Pulsating waves in nonlinear magnetoconvection Physics Letters A, 183, 69-75, 1993
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Matthews PC, Rucklidge AM Travelling and Standing Waves in Magnetoconvection Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 441, 649-658, 1993

Rucklidge AM, Weiss NO, Brownjohn DP, Proctor MRE Oscillations and secondary bifurcations in nonlinear magnetoconvection Geophysical& Astrophysical Fluid Dynamics, 68, 133-150, 1993
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Rucklidge AM Chaos in a low-order model of magnetoconvection Physica D: Nonlinear Phenomena, 62, 323-337, 1993
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Rucklidge AM Chaos in models of double convection Journal of Fluid Mechanics, 237, 209-229, 1992

Rucklidge A, Zaleski S A microcanonical model for interface formation Journal of Statistical Physics, 51, 299-307, 1988
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