Research Areas and Interests
The area of Ivan’s 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 Ivan 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
- Artificial Intelligence and Machine learning
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.
- 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