ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)


Synchronization of excitation waves in a two-layer network of FitzHugh–Nagumo neurons with noise modulation of interlayer coupling parameters

The purpose of this work is to study the possibility of synchronization of wave processes in distributed excitable systems by means of noise modulation of the coupling strength between them. Methods. A simple model of a neural network, which consists of two coupled layers of excitable FitzHugh–Nagumo oscillators with a ring topology, is studied by numerical simulation methods. The connection between the layers has a random component, which is set for each pair of coupled oscillators by independent sources of colored Gaussian noise. Results.

On the conditions for safe connection to hub-cluster power grids

Purpose of this work is studying of the dynamics of a power grid model that results from the expansion of a highly centralized grid, i.e. a hub-cluster, by adding a small subgrid. The main attention is paid to the study of possible power grid operation regimes and their characteristics. Methods. Numerical simulation of power grid operation, the dynamics of which is described by the Kuramoto equations with inertia, is used. Results. Various power grid operation regimes and the boundaries of their existence in the parameter space are given.

Selection of spatial modes in an ensemble of non-locally coupled chaotic maps

Purpose of this work is to determine regularities of formation of spatial structures in an ensemble of chaotic systems with non-local diffusion couplings and to study how these structures depend on the wave response of the digital filter formed by the ensemble couplings structure. Methods. The study was carried out by numerical simulation of an ensemble of logistic maps, calculation of its typical oscillatory regimes and their spectral analysis. The network was considered as a digital filter with a frequency response depending on the coupling parameters.

Study of gyrotron synchronization by an external harmonic signal based on a modified quasi-linear theory

Topic. The paper is devoted to the study of synchronization of a gyrotron by an external harmonic signal. A theoretical study of gyrotron synchronization processes by means of a computational experiment based on certain traditional models of microwave electronics does not provide a complete description of the synchronization pattern. Therefore, the goal of the paper is to develop a modified quasi-linear model based on an approximation of the electron susceptibility by rational functions. Methods.

Simulation of business and financial cycles: Self-oscillation and synchronization

The purpose of this work is to research the phenomena of the self-oscillation and the synchronization for the model of business and financial oscillator, which presented as the system of automatic control. Methods. The research methods are the qualitative and numerical methods of the theory of nonlinear dynamical systems and the theory of the bifurcations. Results. This work presents the model of business and financial oscillators as the phase-controlled oscillator and as the frequency-controlled oscillator.

Synchronization of coupled generators of quasi-periodic oscillations upon destruction of invariant curve

The purpose of this study is to describe the complete picture of synchronization of two coupled generators of quasi-periodic oscillations, to classify various types of synchronization, to study features of occurrence and destruction of multi-frequency quasi-periodic oscillations. Methods. The object of the research is systems of ordinary differential equations of various dimensions. The work uses the fourth-order Runge–Kutta method to solve a system of differential equations.

Synchronization of oscillators with hyperbolic chaotic phases

Topic and aim. Synchronization in populations of coupled oscillators can be characterized with order parameters that describe collective order in ensembles. A dependence of the order parameter on the coupling constants is well-known for coupled periodic oscillators. The goal of the study is to extend this analysis to ensembles of oscillators with chaotic phases, moreover with phases possessing hyperbolic chaos. Models and methods. Two models are studied in the paper.

Approaches to study of multistability in spatio-temporal dynamics of two-age population

Purpose of the work is to study spatio-temporal dynamics of limited two-age structured populations that populate a 2D habitat and capable of long-range displacement of individuals. We proposed the model that is the network of nonlocally coupled nonlinear maps with nonlinear coupling function. Conditions for the emergence of different types of heterogeneous spatial distribution, combining coherent and incoherent regimes in different sites and solitary states are studied. Methods.

Synchronization of oscillators with hyperbolic chaotic phases

Synchronization in a population
of oscillators with hyperbolic chaotic phases is studied for two
models. One is based on the Kuramoto dynamics of the phase oscillators and
on the Bernoulli map applied to these phases. This system
possesses an Ott-Antonsen invariant manifold, allowing for a derivation of a
map for the evolution of the complex order parameter. Beyond a critical coupling strength,
this model demonstrates bistability synchrony-disorder. Another model

Cycles-canards and torus-canards in a weakly inhomogeneous ensemble of FitzHugh–Nagumo neurons with excitatory synaptic couplings

The purpose of this work is to study the dynamics of a weakly inhomogeneous ensemble of three FitzHugh–Nagumo neurons with excitatory synaptic couplings. To single out main types of canard solutions of the system and obtain the regions in parameter space the solutions exist in. Methods. In this paper the dynamics of autonomous systems are studied by using methods based on geometric singular perturbation theory. To study the dynamics of non-autonomous systems we develop an approximate approach and use numerical methods such as obtaining of Poincare maps. Results.