Tel: +44(0) 116 252 5106
PhD, DrSc, Department of Mathematics
- MA2021 (20 credit module), Differential equations and dynamics
- MA2022 (10 credit module), Differential equations and dynamics
- MA3077 (20 credit module), Operations Research
- MA7077 (15 credit module), Operations Research
(ISBN-10: 0521198194 | ISBN-13: 9780521198196)
 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
 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).
 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)
 I.Yu. Tyukin, T. Tyukina, and C. van Leeuwen. Invariant template matching in systems with spatiotemporal coding: a matter for instability. Neural Networks, 22(4): 425-449, 2009 (full text pdf, preprint available at http://arxiv.org/abs/cs.CV/0702082).
 I.Yu. Tyukin, E. Steur, H. Nijmeijer, and C. van Leeuwen. Non-uniform small-gain theorems for systems with unstable invariant sets. SIAM Journal on Control and Optimization, 47(2): 849-882, 2008 (full text pdf, preprint).
 I.Yu. Tyukin, D. V. Prokhorov, and C. van Leeuwen. Adaptive classification of temporal signals in fixed-weights recurrent neural networks: an existence proof. Neural Computation, 20(10):2564-2596, 2008 (full text pdf, preprint available at http://arxiv.org/abs/0705.3370v1).
 I.Yu. Tyukin, D. V. Prokhorov, and C. van Leeuwen. Adaptation and parameter estimation in systems with unstable target dynamics and nonlinear parametrization. IEEE Transactions on Automatic Control, 52(9):1543-1559, 2007 (full text pdf, preprint).
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
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.
Dr I. Tyukin is the Principal Investigator (Knowledge Base Supervisor) in two Knowledge Transfer Partnership (KTP) grants funded by Innovate UK:
- £179,135. KTP009890 between Apical Ltd and the University of Leicester (Visual Intelligence), 2015-2017, Knowledge Base Academic Leader: Prof. A.N. Goran, Company supervisor: Dr. Ilya Romanenko.
- £206,176. 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.
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
- Brain power breakthrough in mathematical modelling , University of Leicester Press Release, September 2007; Alpha Galileo, The world's leading resource for European research news, September 2007.
- Vision requires flexibility, Special Feature of RIKEN (The Institute of Physical and Chemical Research), Brain Science Institute News, Qarterly Leaflet on the Research Highlights, Vol. 36, 2007