Ivan Tyukin


Professor of Applied Mathematics

Head of the Visual Intelligence Lab

Tel: +44(0) 116 252 5106

Email: I.Tyukin@le.ac.uk


Personal details

  • PhD, DrSc, Department of Mathematics
  • My CV



  • MA2021/MA2022 Differential equations and dynamics
  • MA3077/MA7077 Operations Research

Research Highlights in Media


I. Romanenko, I. Tyukin, A.N. Gorban, K. Sofeikov. US Patent number US 10062013B2. Method of Image Processing

I. Romanenko, A.N. Gorban, I. Tyukin. Patent number US10489634B2. Image Processing.

Current grants and projects


  • £1,014,769 FEC [£811,815 from the RC] (Co-Investigator) AH/T001003/1 Arch-I-Scan: Automated recording and machine learning for collating Roman ceramic tablewares and investigating eating and drinking practices, 2019-2022. Principal Investigator - Prof Penelope Allison (University of Leicester).
  • £402,980 FEC [£322,384 from the RC] (Co-Investigator) MR/T017988/1 LOng-Term anatomical fluid dynamics for new Univentricular heartS palliation (LOTUS), 2019-2021. Principal Investigator - Dr Andrea Cangiani (University of Nottingham).

British Health Foundation:

  • £351,400 (Co-Investigator). Insight Research Programme, 2020-2022. Principal Investigator - Prof Tim Coats (University of Leicester).

Innovate UK:

  • £198,735 [A part of a double £384,045 KTP] (Principal Investigator). Innovate UK KTP012250 between TG0 Limited and University of Leicester (Artificial Intelligence technology for learning and recognition of tactile gestures), 2020-2022, Co-Investigator - Dr. Evgeny Mirkes, Dr. Bogdan Grechuk. A
  • £245,824 (Academic Leader). Innovate UK KTP010819 between Photek Limited and University of Leicester (Data Analytics and Mathematical Modelling in High Energy Physics), 2017-2020, Principal Investigator - Dr. Andrey Mudrov

Completed projects

  • £206,176 (Principal Investigator). Innovate UK KTP010522 between Visual Management Systems Limited and the University of Leicester (Security and Visual Intelligence), 2017-2019, Knowledge Base Academic Leader: Prof. A.N. Gorban. Company Supervisor Mr. G. Campbell.
  • £179,135 (Principal Investigator). Innovate UK KTP009890 between Apical Ltd and the University of Leicester (Visual Intelligence), 2015-2017, Knowledge Base Academic Leader: Prof. A.N. Gorban, Company supervisor: Dr. Ilya Romanenko.

Selected Publications

Adaptation book cover

I. Tyukin. Adaptation in Dynamical Systems, Cambridge University Press, 2011

(ISBN-10: 0521198194 | ISBN-13: 9780521198196)







[1] Tyukin IY, Higham DJ, Gorban AN. On Adversarial Examples and Stealth Attacks in Artificial Intelligence Systems. arXiv preprint arXiv:2004.04479. 2020

[2] I. Tyukin, A.N. Gorban, S. Green, D. Prokhorov. Fast Construction of Correcting Ensembles for Legacy Artificial Intelligence Systems: Algorithms and a Case Study, Information Sciences, 485, 230-247, 2019. https://doi.org/10.1016/j.ins.2018.11.057. https://arxiv.org/abs/1810.05593.

[3] A.N. Gorban, A. Golubkov, B. Grechuk, E.M. Mirkes, I.Y. Tyukin. Correction of AI systems by linear discriminants: Probabilistic foundations. Information Sciences, 466, 303-322,  2018. https://doi.org/10.1016/j.ins.2018.07.040

[4] A.N. Gorban, I.Y. Tyukin. Stochastic Separation Theorems. Neural Networks, 94, 255-259, 2017. doi:10.1016/j.neunet.2017.07.014 . Preprint available at https://arxiv.org/abs/1703.01203

[5] A.N. Gorban, I. Tyukin, D. Prokhorov, K. Sofeikov. Approximation with random bases: Pro et contra. Information Sciences, 324-325, 129-145, 2016.  Preprint available at http://arxiv.org/abs/1506.04631

[6] I.Yu. Tyukin, E. Steur, H. Nijmeijer, and Cees van Leeuwen. Adaptive Observers and Parameter Estimation for a Class of Systems Nonlinear in Parameters.  Automatica, 49(8), 2409-2423, 2013, preprint available at  http://arxiv.org/abs/0903.2361

[7] A.N. Gorban, I.Yu. Tyukin,  E. Steur, H. Nijmeijer. Lyapunov-like Conditions of Forward Invariance and Boundedness for a Class of Unstable Systems. SIAM Journal on Control and Optimization, 51(3): 2306-2334, 2013 (preprint available at http://arxiv.org/abs/0901.3577).

[8] E. Steur, I. Tyukin, and  H. Nijmeijer. Semipassivity and synchronization of diffusively coupled neural oscillators. Physica D: Nonlinear Phenomena, 2009. doi:10.1016/j.physd.2009.08.007. (preprint available at http://arxiv.org/abs/0903.3535)


Extended list of publications is available here

Research Areas and Interests

The area of my research interests contains the problems of analysis, modelling and synthesis of fragile, nonlinear, chaotic, meta-stable dynamics; control theory; adaptation in presence of unstable target dynamics, nonlinear parametrisation; state and parameter estimations for systems of ODEs with nonlinear in parameter right-had sides; synchronisation (stable and critical), biologically-inspired systems for processing of the visual information; specific networks with spiking neurons; analysis of dynamics of the spiking neuron models, their properties and possible functions. More recently I became interested in fundamentals of machine learning for problems with high-dimensional feature spaces, computer vision, and intelligent image processing.

They can be characterised by five major topics which are connected to each other by general idea of complex systems approach to understanding, analysis and synthesis of natural and artificial, intelligent systems.

  • Processes and mechanisms of adaptation in complex nonlinear systems
    Systems with nonlinear parametrisation, unstable target dynamics, non-dominating (non-majorating, gentle, non-dominating) adaptation

  • Artificial Intelligence and Machine learning
    Applications to data analytics and modelling, measure concentration effects for high-dimensional data, computer vision and security systems.

  • Synchronisation in nonlinear dynamical systems
    Global, partial, intermittent  synchronisation in the ensembles of linearly and nonlinearly  coupled nonlinear oscillators. Study of connectivity-dependent synchronisation. Adaptive and unstable, multi-stable, alternating synchrony

  • Optimisation algorithms for nonconvex and nonlinear problems
    Parameter estimation of superpositions of nonlinear parameterised functions (with applications to the problem of learning in multilayered pereceptrons)

  • Neuroscience and physics of neuronal cells
    Principles of neuronal processing of  information. Study of properties of the biological cells, analysis of their functions. Structural organisation of the visual system, models system for robust  and adaptive processing (w.r.t modelled uncertainties) of visual information.

Other projects

  • Mathematical Modelling of Adaptation and Decision-Making in Neural Systems
  • Adaptation in Presence of Nonlinear Parameterization
  • Non-uniform Small-gain Theorems and Convergence to Lyapunov-Unstable Invariant Sets

More detailed information about ongoing research projects

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Contact details

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

Tel.: +44 (0)116 229 7407

Campus Based Courses

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

Postgraduate Research: pgrmaths@le.ac.uk

Distance Learning Course  

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