Ivan Tyukin, Ph.D., Dr.Sc.,  RCUK Academic Fellow

Tel: + 44 (0) 116 252 5106, e-mail: I.Tyukin@le.ac.uk

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; 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.

Curriculum Vitae ... 

Selected Publications

Books

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

Journal

[1]  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).

[2]  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).

[3] 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).

[4] S. Gepshtein, I. Tyukin, and M. Kubovy. The economics of motion perception and invariants of visual sensitivity. Journal of Vision, 7(8):8, 1-18, 2007. doi:10.1167/7.8.8. (full text pdf).

[5]  I. Yu. Tyukin and C. van Leeuwen. Decentralized adaptation in interconnected uncertain systems with nonlinear parametrization.  Lecture Notes in Control and Information Sciences, 336:251-270, 2006 (preprint available at http://arxiv.org/abs/math/0606206).

[6]  I.Yu. Tyukin, C. van Leeuwen, and D.V. Prokhorov. Parameter estimation of sigmoid superpositions: Dynamical system approach. Neural Computation, 15(10):2419-2455, 2003 (full text pdf, preprint available at http://arxiv.org/abs/math/0207075).

[7]  I.Yu. Tyukin, D.V. Prokhorov, and V.A. Terekhov. Adaptive control with nonconvex parameterization. IEEE Transactions on Automatic Control, 48(4):554-567, 2003 (full text pdf).

[8]  D.V. Prokhorov, V.A. Terekhov, and Tyukin I.Yu. On the applicability conditions of the adaptive algorithms for the nonconvex problems.  Automation and Remote Control, 63(2):262-279, 2002 (full text pdf).

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

Teaching 

MA2021 (20 credit course), Differential equations and dynamics

MA2022 (10 credit course), Differential equations and dynamics

MA7722 (10 credit course), Introductory mathematical neuroscience