Ivan Tyukin, Ph.D., Dr.Sc.,
Tel: + 44 (0) 116 252 5106,
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.
(ISBN-10: 0521198194 | ISBN-13: 9780521198196)
Published February 2011 | 428 pages | 247 x 174 mm
 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).
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.
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