# School of Mathematics

## 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 @ leeds.ac.uk

### Keywords

Pattern formation

Mode interactions

Quasipatterns

Spatio-temporal chaos

Nonlinear and chaotic dynamics

Heteroclinic networks

Dynamo theory

Magnetoconvection

## 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 arXiv.org

Link to ResearcherID

Link to ResearchGate

## Current postgraduate students

Haifaa Alrihieli (2016)

Andrzej Kucik (2013)

Andrew Mellor (2013)

## Publications

**Rucklidge AM, Knobloch E** Chaos in the Takens–Bogdanov bifurcation with O(2) symmetry *Dynamical Systems*, 1-20, 2016

DOI:10.1080/14689367.2016.1239699

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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

DOI:10.3390/g7030024

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**Subramanian P, Archer AJ, Knobloch E, Rucklidge AM** Three-Dimensional Icosahedral Phase Field Quasicrystal *Physical Review Letters*, **117**, 2016

DOI:10.1103/PhysRevLett.117.075501

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**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

DOI:10.1103/PhysRevE.92.012324

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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

DOI:10.1017/jfm.2015.388

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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

DOI:10.1103/PhysRevE.92.012806

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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

DOI:10.1098/rsif.2014.0735

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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

DOI:10.1103/PhysRevE.90.032704

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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

DOI:10.1002/cplx.21523

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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

DOI:10.1137/130948495

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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

DOI:10.1016/j.enpol.2013.09.033

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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

DOI:10.1103/physrevlett.111.165501

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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

DOI:10.1137/120885371

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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

DOI:10.1080/03091929.2011.643236

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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

DOI:10.1209/0295-5075/102/28012

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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 data*EPSRC 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 Leeds*Energy and People: Futures, complexity and challenges 2012

**Rucklidge AM, Silber M, Skeldon AC** Three-wave interactions and spatiotemporal chaos *Physical Review Letters*, **108**, 2012

DOI:10.1103/PhysRevLett.108.074504

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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

DOI:10.1103/PhysRevE.84.036201

**Botha GJJ, Rucklidge AM, Hurlburt NE** NONLINEAR THREE-DIMENSIONAL MAGNETOCONVECTION AROUND MAGNETIC FLUX TUBES *ASTROPHYS J*, **731**, 2011

DOI:10.1088/0004-637X/731/2/108

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

DOI:10.1007/s00332-010-9063-0

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

DOI:10.1080/14689361003779134

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

DOI:10.1137/080719066

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

DOI:10.1111/j.1365-2966.2008.13359.x

**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

DOI:10.1080/14689360701709088

**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

DOI:10.1103/PhysRevE.75.055203

**Botha GJJ; Rucklidge AM; Hurlburt NE ** *Numerical simulations of sunspots*Proceedings of the International Astronomical Union, 507-509 2006

DOI:10.1017/S1743921307001019

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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

DOI:10.1111/j.1365-2966.2006.10480.x

**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

DOI:10.1080/03091920600565595

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

DOI:10.1063/1.1769111

**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

DOI:10.1016/j.physd.2004.02.002

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

DOI:10.1016/j.physd.2003.12.003

**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

DOI:10.1098/rsta.2003.1267

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

DOI:10.1063/1.1586531

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

DOI:10.1016/S0167-2789(02)00792-3

**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

DOI:10.1103/PhysRevE.66.035201

**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

DOI:10.1016/S0167-2789(00)00124-X

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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

DOI:10.1098/rspa.1999.0498

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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

DOI:10.1016/S0167-2789(98)00174-2

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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

DOI:10.1088/0951-7715/11/5/015

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**Rucklidge AM, Matthews PC** Analysis of the shearing instability in nonlinear convection and magnetoconvection *Nonlinearity*, **9**, 311-351, 1996

DOI:10.1088/0951-7715/9/2/003

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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

DOI:10.1063/1.871699

**Rucklidge AM** Symmetry-breaking instabilities of convection in squares *Proceedings of the Royal Society A: Mathematical, Physical&Engineering Science*, **453**, 107-118, 1996

DOI:10.1098/rspa.1997.0007

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**Rucklidge AM** Chaos in magnetoconvection *Nonlinearity*, **7**, 1565-1591, 1994

DOI:10.1088/0951-7715/7/6/003

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**Matthews PC, Proctor MRE, Rucklidge AM, Weiss NO** Pulsating waves in nonlinear magnetoconvection *Physics Letters A*, **183**, 69-75, 1993

DOI:10.1016/0375-9601(93)90891-3

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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

DOI:10.1098/rspa.1993.0085

**Rucklidge AM, Weiss NO, Brownjohn DP, Proctor MRE** Oscillations and secondary bifurcations in nonlinear magnetoconvection *Geophysical& Astrophysical Fluid Dynamics*, **68**, 133-150, 1993

DOI:10.1080/03091929308203565

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**Rucklidge AM** Chaos in a low-order model of magnetoconvection *Physica D: Nonlinear Phenomena*, **62**, 323-337, 1993

DOI:10.1016/0167-2789(93)90291-8

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**Rucklidge AM** Chaos in models of double convection *Journal of Fluid Mechanics*, **237**, 209-229, 1992

DOI:10.1017/S0022112092003392

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

DOI:10.1007/BF01015333

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**Loutfy RO, Hor AM, Rucklidge A** NEAR-INFRARED PHOTORECEPTOR DEVICES INCORPORATING EVAPORATED CHLOROINDIUM PHTHALOCYANINE. *Journal of imaging science*, **31**, 31-37, 1987

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Postlethwaite CM; Rucklidge AM Spirals and heteroclinic cycles in a spatially extended
Rock-Paper-Scissors model of cyclic dominance.

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