Basic scientific interests are concentrated around problems of qualitative analysis of complex dynamical systems (stability, bifurcations, robustness with respect to perturbation of various kind) in situations when traditional in classic analysis suppositions about smoothness or continuity of dynamical systems under consideration, or about continuity of the state space or the "time component", are not satisfied. Together with M. A. Krasnosel'skii the method of parameter functionalization was developed which allowed to analyze bifurcations of steady states and periodic regimes (a kind of Hopf bifurcation) of non-smooth dynamical systems. Later, with utilization of this method the so-called effect of subfurcation was discovered, i.e. the effect of bifurcating short-living long-periodic regimes of nonsmooth dynamical system in situations when for their smooth analogs the bifurcation of invariant cycles takes place. There were developed essential principles of the theory of stability for the so-called asynchronous systems, i.e. systems describing dynamics of objects updating their states at discrete time instants asynchronously with each other (the typical example of such systems is the computational network). As a bypass result, the algebraic insolubility of the problem of stability analysis for the infinite products of matrices from a finite family was established. Methods of analysis of the dynamics of spatial discretizations for continuous dynamical systems were studied too.

In 1972 graduated from the Mathematical Faculty of the Voronezh State University where specialized in functional analysis, differential equations and control theory. In 1973–1976 studied at the post-graduate courses at the Institute for Control Problems of the Academy of Sciences of the USSR under the supervision of prof. M. A. Krasnosel'skii. The main direction of investigation was the analysis of bifurcation effects accompanying the loss of stability of equilibriums in autonomous or periodic differential or difference equations. It was discovered that typically the loss of stability of the equilibrium in multidimensional case is accompanied by generation of long-periodic solutions with unbounded periods at the moment of branching. This phenomenon got the name subfurcation. In 1976–1988 worked at the National Cardiology Research Center of the Academy of Medical Sciences of the USSR where concentrated on developing computer methods and algorithms for the electrocardiogram parameters measurement. Took part in development of the automated real-time system for diagnostic of cardiac rhythm disorders in the coronary care units. New algorithms were developed for the fast noise removing in electrocardiograms based on the ideas of median and hysteresis filtering. Algorithms for automatic measurement of the parameters of QRS-complexes and P-waves were developed, too, so as alogorithms for edge detection in isotopic images of the hart. Problems of real-time utilization of computer methods of measurement and computation gave a rise to theoretic investigation of asynchronous systems. In parallel, there were continued investigation of the problem of topological classification of singularities of sub-definite mappings. In 1988–1990 worked in the ecology department of the Research Institute for Control Problems "NPO ASU Moskva" where investigated the problem of stability of the phase and frequency desynchronized systems. There were developed symbolical methods of analysis of stability of frequency asynchronous systems. From 1990 until now worked at the Institute for Information Transmission Problems of the Russian Academy of Sciences where continued to investigate asynchronous systems. There were analyzed influence of the conditions of the controllability type on transitional regimes in asynchronous systems. Methods of the theory of stability of asynchronous systems were applied to analysis of flows in data networks and functioning of neural Hopfield-Tank networks. There were started an investigation of the problem of influence of spatial and temporal discretization on the properties of models of continuous systems. In 1979 got the degree of the Candidate of Physical and Mathematical Sciences (an equivalent of the Ph.D. in western countries) and in 1992 got the degree of the Doctor of Physical and Mathematical Sciences.

In different times was the member of Dissertation Soviets (dissertation's qualification board in Russia) at the Yaroslavl State University and at the Institute for Information Transmission Problems. An Associated Editor in the electronic journal "Information processes". Took part in several foreign research grants (Australia, Germany, NATO).

• Kozyakin V., Krasnosel'skii M. The method of parameter functionalization in the Hopf bifurcation problem // Nonlinear Analysis, TMA, 1987, 11, 2, 149–161.

• Institute for Information Transmission Problems, Russian Academy of Sciences