Vol 32, No 3 (2024)

3 June 2024 marks the 70th birthday of Alexander Nikolayevich Pisarchik, a brilliant researcher of international renown in the field of laser physics, nonlinear dynamics and its applications in brain sciences.

The aim of this work is to develop a compact finite-difference approach for modeling the dynamics of predator and prey based on reaction-diffusion-advection equations with variable coefficients. Methods. To discretize a spatially inhomogeneous problem with nonlinear terms of taxis and local interaction, the balance method is used. Species densities are determined on the main grid whereas fluxes are computed at the nodes of the staggered grid. Integration over time is carried out using the high-order Runge-Kutta method. Results. For the case of one-dimensional annular interval, the finite-difference scheme on the three-point stencil has been constructed that makes it possible to increase the order of accuracy compared to the standard second-order approximation scheme. The results of computational experiment are presented and comparison of schemes for stationary and non-stationary solutions is carried out. We conduct the calculation of accuracy order basing on the Aitken process for sequences of spatial grids. The calculated values of the effective order accuracy for the proposed scheme were greater than the standard two: for the diffusion problem, values of at least four were obtained. Decrease was obtained when directional migration was taken into account. This conclusion was also confirmed for non-stationary oscillatory regimes. Conclusion. The results demonstrate the effectiveness of the derived scheme for dynamics of predator and prey system in a heterogeneous environment.

Purpose. The article presents a new method for numerical simulation of quasi-eigenmode oscillations in open resonators of gyrotrons — powerful vacuum generators of electromagnetic waves in the millimeter and submillimeter ranges. The gyrotron cavity has the shape of a weakly inhomogeneous hollow circular metal waveguide. Methods. The proposed approach uses the inhomogeneous string equation with radiation boundary conditions to formulate a nonlinear spectral boundary value problem describing oscillations in a resonator, neglecting the couplings of waves with different radial indices. By linearizing with respect to frequency the radiation boundary conditions, the boundary value problem is reduced to a linear boundary value problem. To discretize this boundary value problem, the finite difference method is used and a linear generalized matrix eigenvalue problem is formulated. This problem is solved by the Arnoldi method with eigenvalues calculation in a shift-invert mode. An iterative algorithm is proposed that makes it possible to sequentially calculate a given number of frequencies and quality factors of quasi-eigenmodes of oscillations. Results. The computer program was developed written in the Wolfram Language and Fortran using the algorithms proposed in the work. The results of test calculations for real gyrotron resonators are presented, which demonstrate the high accuracy of the obtained values of frequencies, quality factors and field distributions of quasi-eigenmode oscillations in the studied resonators. Conclusion. The methods, algorithms and created program proposed in the article can significantly facilitate the process of developing gyrotrons intended for various practical applications and operating in new frequency ranges. The method of iterative refinement of boundary conditions can be generalized to the case of equations of the linear theory of a gyrotron and used to develop new methods for analyzing the starting conditions for the soft self-excitation in gyrotrons — generators.

The purpose of this research is to develop an electrodynamic method for calculating the plasmon spectrum in a three-dimensional structure with a two-dimensional electron gas excited by an incident electromagnetic wave. Methods. The developed method is based on solving integral equations formed with respect to induced currents in the conducting parts of a three-dimensional structure. Results. The convergence of the method and the calculation time were studied. The conditions for the convergence of calculations of higher plasmon resonances in a rectangular structure with a two-dimensional electron gas are determined. The normal incidence of an arbitrarily polarized electromagnetic wave on a rectangle with a two-dimensional gas is studied. The spectra of the absorption, extinction, forward and back scattering cross sections of the incident wave are calculated. Conclusion. It is found that in a rectangular structure containing a two-dimensional electron gas, the spectrum of plasmon resonances is modified in comparison with established by two-dimensional models of problem formulation, in which the structure is assumed to be infinite and homogeneous in one of the directions. It has been established that the incident wave most effectively excites fundamental plasmon modes. Plasmonic modes exhibit strong charge accumulation at the edges of the rectangle, which significantly affects the resonant excitation frequencies of plasmonic modes.

This study aims to consider an ensemble of hippocampal neurons coupled in a ring, which may be responsible for generation of the primary rhythm at limbic epilepsy. Methods. Model equations were solved numerically. To determine the areas of oscillatory and excitable regime existance for a single neuron, the bifurcation analysis for the leakadge conductivity parameter was performed. The coupling delays was not implemented directly, instead, inertia in the synapse was introduced. To determine the stability of generation some couplings were removed and parameter detunig was introduced. Results. In the single neuron model the bistability region was detected, in which a stable focus coexhists with a limit cycle. Two main synchronous regimes were detected. The first regime inherits frequency of individual oscillator, with a relatively small phase shift between oscillators in the ring. The frequency of the second regime depends on the number of neurons in the ring, with the phase shift between neighbor oscillators being equal to ratio of oscillation period and number of neurons. This second regime can occur both for the parameters corresponding to bistabler regime in the individual neuron and for the parameters at which the only existing attractor is stable focus. The second synchronous regime is preserved for parameter detuning of 2% from their absolute values. Conclusion. It was shown that in the mathematical model of the ring of hippocampal neurons, where all the main significant currents are taken into account for individual neurons, and their parameters can vary, there is an oscillatory mode, the frequency of which is determined by the length of the ring and synaptic conductivity, rather than by the parameters individual neuron. In this case, a small change in synaptic conductivity can lead to a sharp (2–7 times) change in the generation frequency.

The purpose of this study is to explore the feasibility of identifying emotional maladjustment using machine learning algorithms. Methods. Electrocardiogram data were gathered using an event-telemetry approach, employing a software and hardware setup comprising a compact wireless ECG sensor (HxM; Zephyr Technology, USA) and a smartphone equipped with specialized software.For constructing the classifier, the following algorithms were employed: logistic regression, easy ensemble, and gradient boosting. The performance of these algorithms was assessed using the f1 metric. Results. It is demonstrated that employing dynamic spectra of the original signals enhances the classification accuracy of the model compared to using the original rhythmograms. Conclusion. A method is proposed for automatically determining the level of emotional maladaptation based on an individual’s cardiorhythmogram. Information from a portable heart sensor, worn by an individual, is transmitted via Bluetooth to a mobile device. Here, the level of emotional maladaptation is assessed through a pre-trained neural network algorithm. When considering a neural network algorithm, it is recommended to employ a classifier trained on spectrograms.

The purpose of this work is to experimentally study, using the inverse spin Hall effect (ISHE), the detection of focused beams of magnetostatic surface waves (MSSW) in integrated YIG (3.9 µm) / Pt (4 nm) thin-film microstructures, where the focusing effect was ensured by the curvilinear shape of the exciting antenna. Make a comparison with the case of detecting MSSWs excited by a rectilinear antenna. Methods. Experiments were carried out using the delay line structures based on the YIG/Pt. The amplitude-frequency characteristics of the YIG/Pt structure and the frequency dependence of the EMF (V(f)) induced in platinum were studied. Results. It was shown that at frequencies f near the long-wavelength limit of the MSSW spectrum, the magnitude of the EMF V(f) generated by a focused MSSW can be several times higher than the values of V(f) in the case of MSSW excitation by a common (straight) antenna. In this case, in the short-wavelength part of the spectrum, on the contrary, the magnitude of the EMF generated by the focused MSSW beam turns out to be noticeably smaller. This behavior is associated with chromatic aberration of the focusing antenna for the MSSW, which manifests itself in the frequency dependence of the focal length of the antenna, which is confirmed by the results of micromagnetic modeling. It is shown that the drop in the EMF signal generated by a focused MSSW beam in the short-wavelength part of the spectrum is associated with the focus reaching the area of the YIG not covered with the Pt film. In this case, the increase in V(f) in the long-wavelength region of the MSSW spectrum is explained by an increase in the linear power density of the MSSW and the formation of caustics under the Pt film. Conclusion. Obtained results can be used for the development of highly sensitive spin wave detectors and the creation of spin logic devices.