Izvestiya of Saratov University.
ISSN 1817-3020 (Print)
ISSN 2542-193X (Online)


Modeling of Epidemics by Cellular Automata Lattices. SIRS Model with Reproduction and Migration

Background and Objectives: Methods of population dynamics give the possibility to analyze many biological phenomena by constructing simple qualitative models, which allow to understand their nature and to predict their behavior. This approach is used to study the spread of epidemics of infectious diseases in biological and human populations. The work considers a modified SIRS model of epidemic spread in the form of a lattice of stochastic cellular automata.

Mutual Synchronization of Dissipatively Coupled Memristive Self-Oscillators

Background and Objectives: Dynamical systems containing memristive elements, i.e. elements with “memory”, represent a special class of dynamical systems that can be named memristive systems. In memristive systems, the synchronization of oscillations has some features. However, a complete description of these features is still lacking. For the most part, this concerns the synchronization of memristive self-oscillators, both identical and with frequency detuning.

Statistics of Poincare Recurrence with Considering Effect of Fluctuations

The basic statistical characteristics of Poincare recurrence are obtained numerically for the logistic map in a chaotic regime. The mean values, variation and recurrence distribution density are calculated and their dependence on a return size is analysed. Afraimovich–Pesin dimension values are obtained. It is verified that the Afraimovich–Pesin dimension corresponds to the Lyapunov exponent. the peculiarities of the influence of noise on the recurrence statistics are studied in local and global approaches.

Synchronous Dynamics of Nephrons Ensembles

In this work, the phenomenon of synchronization of oscillations in the dynamics of nephronic ensembles is studied. It is shown that a large number of structural units on the kidney's surface participate in the formation of synchronous clusters. It is stated that the cluster's size changes in time and the frequency locking for rhythmic processes in the cooperative dynamics of nephrons occurs only during some parts of experimental recordings. 

Complex Waveforms and Synchronization in Functional Model of Vascular Nephron Tree

We suggest functional model that qualitatively describes oscillatory processes in renal autoregulation. Our model consists of ensemble of two-mode oscillators that are coupled by means of two different pathways. The above coupling pathways count both the geometry of ensemble (tree-like structure or local interaction) and the specific action of individual oscillator (energy distribution netrwork or diffusive coupling). We study the typical operating regimes of suggested model as well as transitions between them.

Synchronization of Chimera States in Ensembles of Nonlocally Coupled Cubic Maps

Background and Objectives: Effects of mutual and external synchronization of chimera states are studied in two coupled ensembles of discrete maps. Each of the ensembles is a onedimensional ring of nonlocally coupled cubic maps in the chaotic oscillation mode. In order to create differences in the dynamics of the ensembles when there is no coupling between them, a mismatch is introduced in the parameters of the individual oscillators of the first and second rings. Effects of external and mutual synchronization of chimera states are explored in detail.

On the Theory of Synchronization of a Two-Mode Electron Maser with a Hard Excitation

Background and Objectives: Medium-power (10–100 W) THz continuous-wave electron cyclotron masers (gyrotrons) are of great interest for many applications, such as spectroscopy with dynamic nuclear polarization, plasma diagnostics, non-destructive testing, remote detection of radioactive materials, biomedical applications, etc. For these applications, a high frequency stability is required, with the possibility of frequency tuning within 1–2 GHz.

Spiral Wave Patterns in Two-Layer 2D Lattices of Nonlocally Coupled Discrete Oscillators. Synchronization of Spiral Wave Chimeras

The paper describes the spatio-temporal dynamics of a lattice that is given by a 2D N × N network of nonlocally coupled Nekorkin maps which model neuronal activity. The network behavior is studied for periodic and no-flux boundary conditions. It is shown that for certain values of the coupling parameters, rotating spiral waves and spiral wave chimeras can be observed in the considered lattice. We analyze and compare statistical and dynamical characteristics of the local oscillators from coherence and incoherence clusters of a spiral wave chimera.