# Bifurcation in Dynamical Systems. Deterministic Chaos. Quantum Chaos.

## Experiments on direct chaotic differentially coherent data transmission in a wired communication channel

Methods of differentially coherent information transmission using noise signals are of interest because of the impossibility of implementing the known methods of correlation reception for such signals. With a potentially higher noise immunity compared to the methods of information transmission based on chaotic synchronization, however, they have a feature that does not allow transceivers to be implemented in practice.

## Effective algorithms for solving functional equations with superposition on the example of the Feigenbaum equation

Purpose. New algorithms were consider for functional equations solving using the Feigenbaum equation as an example. This equation is of great interest in the theory of deterministic chaos and is a good illustrative example in the class of functional equations with superposition.

Methods. The article proposes three new effective methods for solving functional equations — the method of successive approximations, the method of successive approximations using the fast Fourier transform and the numerical-analytical method using a small parameter.

## On the typicity of the explosive synchronization phenomenon in oscillator networks with the link topology of the “ring” and “small world” types

Purpose of this study is to investigate the problem of how typical (or, conversely, unique) is the phenomenon of explosive synchronization in networks of nonlinear oscillators with topologies of links such as “ring” and “small world”, and, in turn, how the partial frequencies of the interacting oscillators must correlate with each other for the phenomenon of explosive synchronization in these networks can be possible. Methods.

## Dynamics of the Rabinovich–Fabrikant system and its generalized model in the case of negative values of parameters that have the meaning of dissipation coefficients

Purpose of this work is a numerical study of the Rabinovich–Fabrikant system and its generalized model, which describe the occurrence of chaos during the parametric interaction of three modes in a nonequilibrium medium with cubic nonlinearity, in the case when the parameters that have the meaning of dissipation coefficients take negative values. These models demonstrate a rich dynamics that differs in many respects from what was observed for them, but in the case of positive values of the parameters. Methods.

## On existence of multistability near the boundary of generalized synchronization in unidirectionally coupled systems with complex topology of attractor

Aim of this work is to study the possibility of existence of multistability near the boundary of generalized synchronization in systems with complex attractor topology. Unidirectionally coupled Lorentz systems have been chosen as an object of study, and a modified auxiliary system method has been used to detect the presence of the synchronous regime. Result of the work is a proof of the presence of multistability near the boundary of generalized synchronization in unidirectionally coupled systems with a complex topology of attractor.

## Hunt for chimeras in fully coupled networks of nonlinear oscillators

The purpose of this work is to study the dynamic properties of solutions to special systems of ordinary differential equations, called fully connected networks of nonlinear oscillators. Methods. A new approach to obtain periodic regimes of the chimeric type in these systems is proposed, the essence of which is as follows. First, in the case of a symmetric network, a simpler problem is solved of the existence and stability of quasi-chimeric solutions — periodic regimes of two-cluster synchronization.

## Dynamics of solutions of nonlinear functional differential equation of parabolic type

Purpose of this work is to study the initial-boundary value problem for a parabolic functional-differential equation in an annular region, which describes the dynamics of phase modulation of a light wave passing through a thin layer of a nonlinear Kerr-type medium in an optical system with a feedback loop, with a rotation transformation (corresponds the involution operator) and the Neumann conditions on the boundary in the class of periodic functions.

## New Lagrangian view of vorticity evolution in two-dimensional flows of liquid and gas

Purpose of the study is to obtain formulas for such a speed of imaginary particles that the circulation of the speed of a (real) fluid along any circuit consisting of these imaginary particles changes (in the process of motion of imaginary particles) according to a given time law. (Until now, only those speeds of imaginary particles were known, at which the mentioned circulation during the motion remained unchanged). Method.

## Generalized Rabinovich–Fabrikant system: equations and its dynamics

The purpose of this work is to numerically study of the generalized Rabinovich–Fabrikant model. This model is obtained using the Lagrange formalism and describing the three-mode interaction in the presence of a general cubic nonlinearity. The model demonstrates very rich dynamics due to the presence of third-order nonlinearity in the equations. Methods. The study is based on the numerical solution of the obtained analytically differential equations, and their numerical bifurcation analysis using the MаtCont program. Results.

## Influence of coupling on the dynamics of three delayed oscillators

The purpose of this study is to construct the asymptotics of the relaxation regimes of a system of differential equations with delay, which simulates three diffusion-coupled oscillators with nonlinear compactly supported delayed feedback under the assumption that the factor in front of the feedback function is large enough. Also, the purpose is to study the influence of the coupling between the oscillators on the nonlocal dynamics of the model. Methods. We construct the asymptotics of solutions of the considered model with initial conditions from a special set.