Publications

Journal Articles

• A. Keane, B. Krauskopf and C.M. Postlethwaite
  Climate modelling with delay differential equations
  To appear in Chaos. 2017.
• C.M. Postlethwaite and A.M. Rucklidge
  Spirals and heteroclinic cycles in a spatially extended Rock-Paper-Scissors model of cyclic dominance
  EPL. 117(4) 2017, 48006.
• P. Ashwin and C.M. Postlethwaite
  Quantifying noisy attractors: From heteroclinic to excitable networks
  SIAM Journal on Applied Dynamical Systems. 15(5) 2016, 1989-2016.
• A. Keane, B. Krauskopf and C.M. Postlethwaite
  Investigating irregular behavior in a model for the El Nino Southern Oscillation with positive and negative delayed feedback
  SIAM Journal on Applied Dynamical Systems. 15(3) 2016, 1656-1689.
• R.M. Turner, M.M. Walker and C.M. Postlethwaite
  Literal grid map models for animal navigation: Assumptions and predictions
  Journal of Theoretical Biology. 404 2016, 169-181.
• P. Ashwin and C.M. Postlethwaite
  Designing heteroclinic and excitable networks in phase space using two populations of coupled cells
  Journal of Nonlinear Science. 26(2) 2016, 345-364.
• A. Keane, B. Krauskopf and C.M. Postlethwaite
  Delayed feedback versus seasonal forcing: resonance phenomena in an El Niño Southern Oscillation model.
  SIAM Journal on Applied Dynamical Systems 14(3) 2015, 1229-1257.
• A.S. Purewal, C.M. Postlethwaite and B. Krauskopf
  A global bifurcation analysis of the subcritical Hopf normal form subject to Pyragas time-delayed feedback control.
  SIAM Journal on Applied Dynamical Systems 13(4) 2014, 1879-1915.
• A.S. Purewal, C.M. Postlethwaite and B. Krauskopf
  Effect of delay mismatch in Pyragas feedback control.
  Physical Review E 90 2014, 052905.
• C. M. Postlethwaite and M. Walker,
  A model for navigational errors in complex environmental fields.
  Journal of Theoretical Biology, 363, 2014, 134-144.
• P. Ashwin and C.M. Postlethwaite
  On designing heteroclinic networks from graphs.
  Physica D, 265, 2013, 26-39.
• Claire M. Postlethwaite and Todd Dennis
  Effects of temporal resolution on an inferential model of animal movement. br /> PLoS One, 8(5), 2013 e57640.
• Claire M. Postlethwaite, G.Brown and M.Silber
  Feedback control of unstable periodic orbits in equivariant Hopf bifurcations.
  Philosophical Transactions of the Royal Society A. 371, 2013.
• C.M.Postlethwaite, P.Brown and T.E.Dennis,
  A new multi-scale measure for analysing animal tracking data.
  Journal of Theoretical Biology, 317, 2013, 175-185.
• Vivien Kirk, Claire M. Postlethwaite and Alastair M. Rucklidge
  Resonance in heteroclinic networks.
  SIADS 11(4), 2012, 1360-1401.
• M. Golubitsky and C. M. Postlethwaite,
  Feed-forward networks, center manifolds, and forcing.
  Discrete and Continuous Dynamical Systems, Series A, 32(8), 2012, 2913-2935.
• G. Brown, C. M. Postlethwaite and M. Silber,
  Time-delayed feedback control of unstable periodic orbits near a subcritical Hopf bifurcation.
  Physica D 240, 2011, 859-871.
• C. M. Postlethwaite and M. Walker,
  A geometric model for initial orientation errors in pigeon navigation
  Journal of Theoretical Biology, 269, 2011, 273-279.
• Claire M. Postlethwaite
  A new mechanism for stability loss from a heteroclinic cycle.
  Dynamical Systems: An International Journal, 25(3), 2010, 305-322. PDF (348KB)
• V. Kirk, E. Lane, C. M. Postlethwaite, A. M. Rucklidge, and M. Silber
  A mechanism for switching near a heteroclinic network.
  Dynamical Systems: An International Journal, 25(3), 2010, 323-349. PDF (620KB)
• Claire M. Postlethwaite and J.H.P. Dawes
  Resonance bifurcations from robust homoclinic cycles.
  Nonlinearity 23, 2010, 621-642. PDF (572KB)
• Claire M. Postlethwaite, Tiffany M. Psemeneki, Jangir Selimkhanov, Mary Silber and Malcolm A. MacIver
  Optimal movement in the prey strikes of weakly electric fish: A case study of the interplay of body plan and movement capability.
  Roy. Soc. Interface, 6(34), 2009, 417-433. PDF (2.3MB)
• C. M. Postlethwaite
  Stabilization of long-period periodic orbits using time-delayed feedback control.
  SIADS, 8, 2009, 21-39. PDF (432KB)
• Claire M. Postlethwaite and Mary Silber
  Stabilizing unstable periodic orbits in the Lorenz equations using time-delayed feedback control.
  Phys. Rev. E, 76, 2007, 056214. http://arxiv.org
• Claire M. Postlethwaite and Mary Silber
  Spatial and temporal feedback of traveling wave solutions of the two-dimensional complex Ginzburg-Landau equation.
  Physica D, 236, 2007, 65-74. http://arxiv.org
• C. M. Postlethwaite and J. H. P. Dawes
  A codimension-two resonant bifurcation from a heteroclinic cycle with complex eigenvalues.
  Dynamical Systems: An International Journal, 21(3), 2006, 313-336. PDF (292KB)
• C. M. Postlethwaite and J. H. P. Dawes
  Regular and irregular cycling near a heteroclinic network.
  Nonlinearity, 18, 2005, 1477-1509.
• J. H. P. Dawes, C. M. Postlethwaite and M. R. E. Proctor
  Instabilities induced by a weak breaking of a strong spatial resonance.
  Physica D, 191, 2004, 1-30.

Book chapters

• M. Golubitsky, C. Postlethwaite, L-J. Shiau and Y. Zhang
  The feed-forward chain as a filter amplifier motif.
  In: Coherent Behavior in Neuronal Networks. (K. Josic, M. Matias, R. Romo, and J. Rubin, eds.) Springer, 2009, 95-120. PDF (1.1MB)
• A.S. Purewal, B. Krauskopf and C.M. Postlethwaite
  Global effects of time-delayed feedback control applied to the Lorenz system
  In: Control of Self-Organizing Nonlinear Systems. (E. Schöll, S.H.L. Klapp and P. Hövel, eds.), Springer Series in Synergetics, Springer-Verlag (2015, to appear)

Conference Proceedings

• J.E.Paterson, M.O.J.Thomas, C.M.Postlethwaite and S.Taylor
  The internal disciplinarian: Who is in control?
  In: S. Brown, S. Larsen, K. Marrongelle, and M. Oehrtman (Eds.), Proceedings of the 14th Annual Conference on Research in Undergraduate Mathematics Education 2, 2011, 354-368. Portland, Oregon.

Submitted or in preparation

• R.M. Turner, M.A. Shooshtari and C.M.Postlethwaite
  Distinguishing between navigation models from animal tracks Submitted to Movement Ecology
• P. Ashwin and C.M.Postlethwaite
  Sensitive finite state computations using a distributed network with a noisy network attractor Submitted to IEE Transactions on Neural Networks and Learning Systems
• C.M.Postlethwaite and A.M. Rucklidge
  A trio of heteroclinic bifurcation in spatially extended Rock-Paper Scissors. In preparation

Seminars and Presentations

• `Heteroclinic cycles and spiral waves in Rock-Paper-Scissors'. Mathematical Biosciences Institute, Ohio, USA, Sept 2017.
• `Designing noisy networks'. Minisymposium Presentation, SIAM conference on Applications of Dynamical Systems, Utah, USA, May 2017.
• `Noisy attractors: modelling using heteroclinic and excitable networks'. Invited plenary talk, annual meeting of ANZIAM, Adelaide, Feb 2017.
• `Why did the pigeon cross the road? Mathematical modelling of animal behaviour'. Invited talk at ANZIAM MathBio Special interest group, Adelaide, Feb 2017.
• `Navigational errors in complex environmental fields'. RIN conference, London, April 2016.
• `Noisy attractors: modelling using heteroclinic and excitable networks'. Invited plenary talk, annual meeting of NZMS, Christchurch, Dec 2015.
• `Why did the pigeon cross the road? Mathematical modelling of animal behaviour'. Public lecture, University of Auckland, Nov 2014.
• 'Heteroclinic networks: stability, switching and memory'. Nottingham University, UK, May 2014.
• 'Heteroclinic networks: stability, switching and memory'. Exeter University, UK, May 2014.
• 'Team-based learning in postgraduate mathematics'. Leeds University, UK, April 2014.
• 'Heteroclinic networks: stability, switching and memory'. Leeds University, UK, April 2014.
• `A mathematical model of pigeon navigation'. ANZIAM annual conference, Roturua, New Zealand, February 2014.
• `Why did the pigeon cross the road? Mathematical modelling of animal behaviour'. Invited public lecture in RSNZ 10x10 Mathematics of Planet Earth series. Napier, NZ, November 2013.
• `Resonance in heteroclinic networks'. Invited speaker in minisymposium on Heteroclinic Cycles, American Institute of Mathematical Sciences meeting, Orlando, USA, July 2012.
• `Feedback control of unstable periodic orbits arising from equivariant Hopf bifurcations'. Invited plenary speaker at International Conference on Complex Delayed Systems, Mallorca, Spain, June 2012.
• `Resonance in heteroclinic networks'. Invited plenary speaker at conference `Progress and Problems in Dynamical Systems’, Houston, USA, May 2012.
• `A geometric model for initial orientation errors in pigeon navigation'. Seminar series, School of Biological Science, University of Auckland, NZ, August 2011.
• `Optimal movement in the prey capture behaviour of weakly electric fish'. Seminar series, Department of Engineering Science, University of Auckland, NZ, August 2011.
• `Switching on a heteroclinic network'. Minisymposium Presentation, SIAM conference on Applications of Dynamical Systems, Utah, USA, May 2011.
• `Dynamics of heteroclinic cycles and networks'. Minisymposium Organiser, SIAM conference on Applications of Dynamical Systems, Utah, USA, May 2011.
• `A geometric model for initial orientation errors in pigeon navigation'. Contributed presentation, Royal Society meeting on Orientation and Navigation, UK, April 2011.
• `Bifurcations of heteroclinic cycles'. NZMC conference, Otago University, NZ, December 2010.
• `What matters to an Applied Mathematician? A conversation that explores this theme' (with Judy Paterson). Keynote Presentation at a teacher’s professional development day, Auckland Mathematics Association, NZ, November 2010.
• `Optimal movement in the prey capture behaviour of weakly electric fish'. Seminar series, School of Biological Science, University of Auckland, NZ, September 2010.
• `A geometric model for initial orientation errors in pigeon navigation'. Poster presentation, SIAM Conference on Life Sciences, Pittsburgh, USA, July 2010.
• `Bifurcations from robust heteroclinic cycles'. Seminar series, Leeds University, UK, January 2010.
• `Switching on heteroclinic networks'. Poster presentation, NZMC conference, Massey University, NZ, December 2009.
• 'Feedback control of long-period periodic orbits'. Contributed Presentation, SIAM conference on Applications of Dynamical Systems, Utah, USA, May 2009.
• 'Feedback control of unstable periodic orbits'. Special session on Ergodic Theory and Dynamical Systems, ANZMC conference, University of Canterbury, Christchurch, NZ, December 2008.
• 'Optimal movement in the prey capture behaviour of weakly electric fish'. Special session on Biological Modelling, ANZMC conference, University of Canterbury, Christchurch, NZ, December 2008.
• 'Optimal movement in the prey capture behaviour of weakly electric fish'. Applied Mathematics Seminar, University of Auckland, NZ, October 2008.
• 'Optimal movement and motor capacity in a short-range aquatic predator'. Society for Mathematical Biology Conference, University of Toronto, Toronto, Canada, August 2008.
• 'Feedback control of unstable patterns and periodic orbits'. DAMTP seminar series, University of Cambridge, UK, July 2008.
• 'Feedback control of unstable patterns and periodic orbits'. AMS Central sectional meeting, Chicago, USA, October 2007.
• 'Controlling travelling waves of the complex Ginzburg-Landau equation with spatial feedback'. Poster presentation, GRC Nonlinear Science, Maine, USA, June 2007.
• 'Controlling travelling waves of the complex Ginzburg-Landau equation with spatial feedback'. Contributed Presentation, SIAM conference on Applications of Dynamical Systems, Utah, USA, May 2007.
• 'Controlling pattern formation'. Short presentation, Introductory Workshop on Dynamical Systems with Emphasis on Extended Systems, MSRI, Berkeley, USA, January 2007.
• 'Controlling travelling waves of the complex Ginzburg-Landau equation with spatial feedback'. Connections for Women: Dynamical Systems, MSRI, Berkeley, USA, January 2007.
• 'Cycling Cycles: Dynamics near a Heteroclinic Network'. Applied Mathematics Colloquium, Northwestern University, USA, October 2006.
• 'Cycling Cycles: Dynamics near a Heteroclinic Network'. Presentation at the Isaac Newton Institute Programme 'Pattern Formation in Large Domains', UK, October 2005.
• 'A Codimension Two Resonant Bifurcation from a Heteroclinic Cycle with Complex Eigenvalues'. Contributed Presentation, SIAM conference on Applications of Dynamical Systems, Utah, USA, May 2005.
• 'Cycling Cycles: Dynamics near a Heteroclinic Network'. Poster presentation at Coupled 60 workshop, University of Houston, Texas, USA, February 2005.
• 'Cycling Cycles: Dynamics near a Heteroclinic Network'. Applied Mathematics Seminar Series, Exeter, UK, November 2004.
• 'Cycling Cycles: Dynamics near a Heteroclinic Network'. DAMTP 2nd year PhD Seminar Series, Cambridge, UK, May 2004.
• 'Cycling Cycles: Dynamics near a Heteroclinic Network'. LMS PANDA meeting, Cambridge, UK, December 2003.
• 'Heteroclinic Networks in Rotating Convection'. AFD/NLP Group Seminar Series, Cambridge, UK, October 2003.
• 'Heteroclinic Networks in Rotating Convection'. Poster presentation at Workshop on Dynamics and Bifurcations of Patterns, Colorado State University, USA, May 2003.
• 'Heteroclinic Networks in Rotating Convection'. Poster presentation at SIAM conference on Applications of Dynamical Systems, Utah, USA, May 2003.