Dynamics of Complex Systems

Research directions of the group include detection and analysis of coherent structures in nonlinear PDEs Aperiodic tilings, strange attractors and topological rigidity of affine endomorphisms of nilmanifolds, Aperiodic patterns, classification of structured but non-repeating tilings and patterns, models for quasicrystals, chaotic attractors, dynamics of complex systems of chemical, physical and biological kinetics, dimensionality reduction and dynamical methods in data mining and adaptation and control in dynamical systems, brain dynamics.

Current members

 

Some recent publications

  1. I. Prokin, I. Tyukin, V. Kazantsev, Phase Selective Oscillations in Two Noise Driven Synaptically Coupled Spiking Neurons, International Journal of Bifurcation and Chaos 07/2015; 25(7):1540005.
  2. NB Budanur, P Cvitanović, RL Davidchack, E Siminos, Reduction of SO (2) symmetry for spatially extended dynamical systems, Physical review letters 114 (8) (2015), 084102.
  3. A.N. Gorban, N. Jarman, E. Steur, C. van Leeuwen, I. Tyukin. Leaders do not look back, or do they? Mathematical Modelling of Natural Phenomena, 10 (3), 212-231, 2015
  4. N. Jarman, C. Trengove, E. Steur, I. Tyukin, C. van Leeuwen, Spatially constrained adaptive rewiring in cortical networks creates spatially modular small world architectures, Cognitive Neurodynamics, Springer, 2014, 1-19.
  5. D.S. Goldobin, Noise Can Reduce Disorder in Chaotic Dynamics,, The European Physical Journal Special Topics 223 (8) (2014), 1699-1709.

  6. .S. Goldobin, Uncertainty principle for control of ensembles of oscillators driven by common noise, The European Physical Journal Special Topics 223 (4) (2014), 677-685.
  7. A.N. Gorban, I. Tyukin, E. Steur, and H. Nijmeijer, Lyapunov-like conditions of forward invariance and boundedness for a class of unstable systems, SIAM J. Control Optim.  51 (3) (2013), 2306-2334.
  8. A. N. Gorban, Thermodynamic Tree: The Space of Admissible Paths , SIAM J. Applied Dynamical Systems 12 (1) (2013), 246-278.
  9. A Clark, J Hunton, Tiling spaces, codimension one attractors and shape, New York J. Math. 18 (2012) 765-796.
  10. P. Cvitanović, R. L. Davidchack, E. Siminos. On the state space geometry of the Kuramoto-Sivashinsky flow in a periodic domain. SIAM J. Appl. Dyn. Syst. 9(1), pp. 1–33 (2010).
  11. I. Tyukin. Adaptation in Dynamical Systems, Cambridge University Press, 2011
  12. A. N. Gorban, A. Zinovyev, Principal manifolds and graphs in practice: from molecular biology to dynamical systems, International Journal of Neural Systems, Vol. 20, No. 3 (2010) 219–232.
  13. A. Clark, R. Fokkink, Self-duality and codings for expansive automorphisms, Nonlinearity 22 (7) (2009), 1663-1671.
  14. I.Yu. Tyukin, E. Steur, H. Nijmeijer, and C. van Leeuwen. Nonuniform small-gain theorems for systems with unstable invariant sets. SIAM Journal on Control and Optimization, 47(2):849-882, 2008.
  15. E. Steur, I. Tyukin, and H. Nijmeijer. Semi-passivity and synchronization of neuronal oscillators. Physica D: Nonlinear Phenomena, 21(1):2119-2128, 2009.

Current PhD students

Sheila McCann, Dina Abuzaid, Dave Packwood, Jamie Walton, Andrew Peden, David  Fairhurst

Previous PhDs:
  • David Fletcher, PhD 2011, "Construction operations to create new aperiodic tilings: local isomorphism classes and simplified mathcing rules"
  • Jonathan Crofts, PhD 2007, "Efficient method for detection of periodic orbits in chaotic maps and flows"
  • Muhammad Shahzad – PhD 2011, “Slow Invariant Manifold and its approximations in kinetics of catalytic reactions”

Grants

  • Nov 2008- Nov 2011, EPSRC EP/G006377/1, "Foliations: solenoids, regularity and ends," Value: £265,290.90; PI: A. Clark
  • 2004-2007: EPSRC GR/S98986/01: “Developing Efficient Method for Locating Periodic Orbits in Hamiltonian Maps and Flows", Value: £70k,  PI R. Davidchack
  • "Activity Patterns in Culture Neuronal Networks: Analysis and Control" PI A.N. Gorban, (Leicester) Co-I: V.B. Kazantsev  (Institute of Applied Physics, Russian Academy of Science, Nizhny Novgorod, Russia), I.Yu. Tyukin (Leicester, UK), R. Quiroga (Leicester, UK) Duration: 2009 - 2011 Source of funding: The Royal Society, UK: International Joint Project
  • "Modularity, Abstraction and Robustness of Network Models in Molecular Biology" PI: A.N. Gorban (Leicester, UK), Co-I:  O. Radulescu (Rennes, France) Duration: 2007 - 2008 Source of funding: British Council: Alliance program
  • "Mathematical Modelling of Adaptation and Decision-Making in  Neural Systems", PI: I.Yu. Tyukin (Leicester, UK), Co-I: Cees van Leeuwen  (RIKEN Brain Science Institute, Wako-shi, Japan), A.N. Gorban (Leicester, UK) Duration: 2007 - 2009, Source of funding: The Royal Society, UK: International Joint UK-Japan Project
  • EPSRC grant for Workshop on Aperiodic Order, September 2009
  • EPSRC grant for Workshop "Coping with Complexity: Model Reduction and Data Analysis", August 2009

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Contact details

Department of Mathematics
University of Leicester
University Road
Leicester LE1 7RH
United Kingdom

Tel.: +44 (0)116 252 3917
Fax: +44 (0)116 252 3915

Campus Based Courses

Undergraduate: mathsug@le.ac.uk
Postgraduate Taught: mathspg@le.ac.uk

Postgraduate Research: pgrmaths@le.ac.uk

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