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


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.

Synchronization of infections spread processes in populations interacting: Modeling by lattices of cellular automata

Purpose. Study of synchronization of oscillations in ensembles of probabilistic cellular automata that simulate the spread of infections in biological populations. Method. Numerical simulation of the square lattice of cellular automata by means of the Monte Carlo method, investigation of synchronization of oscillations by time-series analisys and by the coherence function. Results. The effect has been found of synchronization of irregular oscillations, similar to the phenomenon of synchronization of chaos in dynamical systems.

Threshold stability of the synchronous mode in a power grid with hub cluster topology

The main purpose of this paper is to investigate the dynamics of the power grid model with hub cluster topology based on the Kuramoto equations with inertia. It is essential to study the stability of synchronous grid operation mode and to find conditions of its global stability. The conditions that ensure establishment of the synchronous mode instead of coexisting asynchronous ones are considered. Methods. In this paper we use numerical modelling of different grid operation modes.

Frequency entrainment and anti-entrainment of coupled active rotators synchronized by common noise

Topic and Aim. We study the effect of common noise on the ensemble of coupled active rotators. Such a noise always has a synchronizing effect on the system, whereas the coupling may be attracting (synchronizing) or repulsing