Ivan Tyukin

 Page picture


Ivan Tyukin, Ph.D., Dr.Sc., 


Tel: + 44 (0) 116 252 5106,

 e-mail: I.Tyukin@le.ac.uk

   Google Scholar Profile

Curriculum Vitae ... 

Leicester Mathematics on Google Scholar 

Research 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 parametrization; state and parameter estimations for systems of ODEs with nonlinear in parameter right-had sides; synchronization (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. They can be characterized by four 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 parametrization, unstable target dynamics, non-dominating (non-majorating, gentle, non-dominating) adaptation 

  • Synchronization in Nonlinear Dynamical Systems. Global, partial, intermittent  synchronization in the ensembles of linearly and nonlinearly  coupled nonlinear oscillators. Study of connectivity-dependent synchronization. Adaptive and unstable, multi-stable, alternating synchrony 

  • Optimization algorithms for nonconvex and nonlinear problems. Parameter estimation of superpositions of nonlinear parameterized 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 organization of the visual system, models system for robust  and adaptive processing (w.r.t modelled uncertainties) of visual information.



Selected Publications


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

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

Published February 2011 | 428 pages | 247 x 174 mm

Adaptation book cover



[1] 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

[2] 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).

[3] 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)

[4] 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): 425-4492009 (full text pdf, preprint available at http://arxiv.org/abs/cs.CV/0702082).

[5]  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).

[6]  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).

[7] 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).


Extended list of publications is available here


Current 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



Please follow this link for a more detailed information about ongoing research projects



Press Releases

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



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 

Share this page:

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: pgrmeccluster@le.ac.uk

Distance Learning Course  

Actuarial Science: actsciadmin@le.ac.uk