Research Interests

The area of my research interests contains the problems of analysis, modelling and synthesis of fragile, nonlinear, chaotic, meta-stable dynamics, adaptation in presence of unstable target dynamics, nonlinear parametrization, synchronization (stable and critical), biologically-inspired systems for processing of the visual information, computer vision, networks of interconnected dynamical systems, analysis of dynamics of the spiking neuron models, their properties and possible functions, algorithms for machine learning and data analysis in high dimensions. They can be characterized by six 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.

1. Machine Learning and Data Analysis in High dimensions. Exploiting measure concentration effects for development and analysis of efficient algorithms for machine learning and data analytics in high dimensions.

2. Processes and Mechanisms of Adaptation in Complex Nonlinear Systems. Systems with nonlinear parametrization, unstable target dynamics, non-dominating (non-majorating, gentle, non-dominating) adaptation

3. 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.

4. Optimization algorithms for nonconvex and nonlinear problems. Parameter estimation and inverse problems involving systems of ordinary differential equations with nonlinear in parameter right-hand side.

5. Analysis of dynamical systems with unstable and semi-stable attractors. Extension of the method of Lyapunov functions for systems with weakly attracting  (in Milnor sense) invariant sets, first method of Lyapunov for non-hyperbolic equilibria, non-uniform small-gain theorems.

6. 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.

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

Tel.: +44 (0)116 229 7407

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