Synchronization of nonlinearly coupled networks based on circle criterion.

The problem of synchronization in networks of linear systems with nonlinear diffusive coupling and a connected undirected graph is studied. By means of a coordinate transformation, the system is reduced to the form of mean-field dynamics and a synchronization-error system. The network synchronization conditions are established based on the stability conditions of the synchronization-error system obtained using the circle criterion, and the results are used to derive the condition for synchronization in a network of neural-mass-model populations with a connected undirected graph.

Prediction of the COVID-19 spread in Russia based on SIR and SEIR models of epidemics.

An attempt is made to use the simplest epidemic models: SIR and SEIR to predict the spread of COVID-19 in Russia. Simplicity and a small number of parameters are very significant advantages of SIR and SEIR models in conditions of a lack of numerical initial data and structural incompleteness of models. The forecast of distribution of COVID-19 in Russia is carried out according to public data sets from March 10 to April 20, 2020.

Horizons of cybernetical physics.

The subject and main areas of a new research field-cybernetical physics-are discussed. A brief history of cybernetical physics is outlined. The main areas of activity in cybernetical physics are briefly surveyed, such as control of oscillatory and chaotic behaviour, control of resonance and synchronization, control in thermodynamics, control of distributed systems and networks, quantum control.

Dynamics of non-stationary processes that follow the maximum of the Rényi entropy principle.

We propose dynamics equations which describe the behaviour of non-stationary processes that follow the maximum Rényi entropy principle. The equations are derived on the basis of the speed-gradient principle originated in the control theory. The maximum of the Rényi entropy principle is analysed for discrete and continuous cases, and both a discrete random variable and probability density function (PDF) are used.

Adaptive synchronization in delay-coupled networks of Stuart-Landau oscillators.

We consider networks of delay-coupled Stuart-Landau oscillators. In these systems, the coupling phase has been found to be a crucial control parameter. By proper choice of this parameter one can switch between different synchronous oscillatory states of the network.

Synchronization of nonlinear systems under information constraints.

A brief survey of control and synchronization under information constraints (limited information capacity of the coupling channel) is given. Limit possibilities of nonlinear observer-based synchronization systems with first-order coders or full-order coders are considered in more detail. The existing and new theoretical results for multidimensional drive-response Lurie systems (linear part plus nonlinearity depending only on measurable outputs) are presented.

Yakubovich's oscillatority of circadian oscillations models.

The testing procedure of Yakubovich's oscillatority property is presented. The procedure is applied for two models of circadian oscillations [J.C.

Controlled synchronization under information constraints.

A class of controlled synchronization systems under information constraints imposed by limited information capacity of the coupling channel is analyzed. It is shown that the framework proposed by Fradkov, [Phys. Rev.

Chaotic observer-based synchronization under information constraints.

Limitations of observer-based synchronization systems under information constraints (limited information capacity of the coupling channel) are evaluated. We give theoretical analysis for multidimensional drive-response systems represented in the Lurie form (linear part plus nonlinearity depending only on measurable outputs). It is shown that the upper bound of the limit synchronization error (LSE) is proportional to the upper bound of the transmission error.

Control of chaos: methods and applications in mechanics.

A survey of the field related to control of chaotic systems is presented. Several major branches of research that are discussed are feed-forward ('non-feedback') control (based on periodic excitation of the system), the 'Ott-Grebogi-Yorke method' (based on the linearization of the Poincaré map), the 'Pyragas method' (based on a time-delayed feedback), traditional for control-engineering methods including linear, nonlinear and adaptive control. Other areas of research such as control of distributed (spatio-temporal and delayed) systems, chaotic mixing are outlined.