卷 33, 编号 1 (2025)
Editorial
50th anniversary of the discovery of Feigenbaum's patterns
摘要
In 1975, while experimenting with a pocket programmable calculator, American physicist Mitchell Feigenbaum discovered the universal patterns of transition to chaos through period doubling bifurcations, which now bear his name.
Izvestiya VUZ. Applied Nonlinear Dynamics. 2025;33(1):5-8
5-8
Bifurcation in dynamical systems. Deterministic chaos. Quantum chaos
Intermittent behavior near the boundary of generalized synchronization in unidirectionally coupled time-delayed systems
摘要
The aim of the work is an analysis of characteristics of intermittent behavior taking place near the boundary of generalized synchronization in unidirectionally coupled time-delayed generators. The case of interaction of systems characterized by different numbers of positive Lyapunov exponents is considered. To determine the lengths of characteristic phases of the system behavior the auxiliary system method has been used. The result of the work is the determination of the type of intermittency taking place near the boundary of generalized synchronization. In this case by calculation the statistical characteristics of the laminar phase lengths (distributions of the laminar phase lengths and the dependencies of the mean lengths of the laminar phases on the criticality parameters) it has been found that near the boundary of the synchronous regime the on-off intermittency is observed. It has been shown that the intermittent generalized synchronization in time-delayed systems is characterized by multistability. For these purposes a time-averaged measure of multistability depending on the value of the coupling parameter between systems has been calculated and compared with the behavior of the spectrum of Lyapunov exponents. It has been found that the multistability measure can be used to detect the generalized synchronization in time-delayed systems.
Izvestiya VUZ. Applied Nonlinear Dynamics. 2025;33(1):9-18
9-18
Applied problems of nonlinear oscillation and wave theory
Anisotropy and amplification of terahertz electromagnetic response enabled by direct electric current in graphene
摘要
The purpose of this study is to investigate the polarization conversion and amplification of electromagnetic terahertz (THz) wave incident normally upon graphene monolayer with direct electric current flowing at arbitrary angle to the elecric vector of incident wave. Methods. The expressions for the elements of the dynamic conductivity tensor of graphene were obtained in hydrodynamic approximation. The electromagnetic response is calculated by solving the Maxwell equations with standard boundary conditions for lateral components of the electric and magnetic fields. Results. It is shown that the dynamic conductivity of graphene depends on value and direction of the electron drift velocity even in the absence of the spatial dispersion. This results in the polarization conversion of electromagnetic radiation at THz frequencies. The real parts of elements of graphene dynamic conductivity tensor can become negative which leads to the amplification of THz oscillations. Conclusion. The polarization conversion and amplification of electromagnetic THz wave incident upon graphene with direct electric current is demonstrated. Polarization conversion efficiency can be as high as 97 percent.
Izvestiya VUZ. Applied Nonlinear Dynamics. 2025;33(1):19-26
19-26
Reconstruction of self-oscillating systems with delay time modulation
摘要
The aim of our research is to study the possibility of reconstruction from time series the self-oscillating systems with variable time delay, demonstrating regimes of turbulent and laminar chaos. Methods. The object of study is self-oscillating systems described by delay-differential equations, in which the delay time is modulated by an external periodic signal. The possibility of estimating the parameters of systems with delay time modulation from their time series is considered using the known method for reconstructing systems with constant delay time, which is based on statistical analysis of time intervals between all possible pairs of extrema in time series. A new method for estimating the parameters of systems with variable delay time is proposed, based on statistical analysis of time intervals between two successive extrema in time series. Results. It is shown that in some cases the known methods for reconstructing systems with constant delay time are also effective for reconstructing systems with varying delay time. With their help, one can estimate the mean delay time and recove the nonlinear function of the system. The proposed method, aimed at application to time-delay systems with delay time modulation, allows one to estimate the frequency and amplitude of delay time modulation. Conclusion. The obtained results are of interest to various scientific disciplines that study systems with variable delay times based on their time series.
Izvestiya VUZ. Applied Nonlinear Dynamics. 2025;33(1):27-37
27-37
Multistability of synchronous modes in a multimachine power grid with a common load and their global and non-local stability
摘要
The purpose of this work is studying the dynamics of the power grid consisting of an arbitrary number of synchronous generators supplying a common passive linear load. We focus on searching the conditions for the existence and stability of synchronous modes, i.e. the main operating modes of a power grid. The possibility of the existence of non-synchronous (quasi-synchronous and asynchronous) modes is investigated. Methods. To study the dynamics of a power grid we use the effective network model in the form of an ensemble of globally coupled nodes-generators. The state of every node is described by the swing equation. The approach for reducing the effective network to the network with a hub topology (star topology) is proposed. We use numerical methods to construct a partition of the parameter space into areas with different operating modes of the power grid. Results. The conditions for the existence, stability and multistability of synchronous modes are obtained. The main characteristics of these modes are considered, such as the power supplied by generators to the grid and the distribution of currents along transmission lines. We constructed the partition of the power gird parameter space into areas with different dynamics. Conclusion. The power grid consisting of an arbitrary number of synchronous generators supplying a common passive linear load has been studied. We shown the presence of two types of synchronous modes: homogeneous and inhomogeneous. The first is characterized by equal powers and currents flowing through all load supply paths except one. The second provides another additional path, which differs from the others in current and transmitted power. Moreover, the currents flowing along the same path, but in various modes, differ. The presence of high multistability of inhomogeneous synchronous modes has been established. The possibility of coexistence of homogeneous and inhomogeneous synchronous modes, as well as quasi-synchronous and asynchronous modes, is shown. In the power grid parameters space we found areas corresponding both the existence of only synchronous modes and their coexistence with quasi-synchronous and/or asynchronous modes.
Izvestiya VUZ. Applied Nonlinear Dynamics. 2025;33(1):38-68
38-68
Innovations in applied physics
Model of 2D-imaging system using correlation-based reception for image synthesis of radio light sources
摘要
The purpose of this work is to create a model of a system for constructing 2D images of radio light sources, where reception is based on correlation processing of signals coming from receiving antennas placed apart in space. In this article radio light refers to ultrawideband noise-like microwave radiation. Methods. To achieve this goal, a method for constructing an image is proposed and its implementation is tested using computer modeling of an imaging system. Results. It is shown how, using correlation signal processing methods, it is possible to construct 2D images of radio light sources using the example of computer modeling. Images of radio light sources were obtained, where it is possible to observe in one image two sources with a difference in the level of the emitted signal of 12 dB. Conclusion. A computer model of a correlation-based radio light receiver has been developed, which makes it possible to evaluate the influence of the number of antennas on the final image, as well as to obtain images of several radio light sources. The results of the computer simulation can be used to create a model of a real imaging system for radio light based on correlation processing.
Izvestiya VUZ. Applied Nonlinear Dynamics. 2025;33(1):69-81
69-81
Nonlinear dynamics and neuroscience
Effects of the dynamics of noise-induced calcium signals in a biophysical model of the astrocytic process
摘要
The purpose of this work is to study the effects of spatio-temporal dynamics of spontaneous calcium signaling in the morphological structure of an astrocyte at the subcellular level using biophysical mathematical modeling methods. Methods. This work proposes a biophysical multicompartmental model of noise-induced calcium dynamics in the astrocytic process. The model describes the process of generation of spontaneous Ca2+ signals induced by the stochastic activation of voltage-dependent Ca2+ channels on the plasma membrane of the astrocyte. The model allows us to study the dynamics of the propagation of spontaneous local Ca2+ signals and the mechanisms of formation of spatial Ca2+ patterns in the astrocytic process. Results. The developed model enables studying the influence of morphology and intracellular biophysical mechanisms on the characteristics of spontaneous noise-induced Ca2+ signaling in the astrocytic process. The parameter ranges at which the model qualitatively reproduces the spontaneous Ca2+ activity at the subcellular level observed in experimental studies have been specified. The characteristics of noise-induced Ca2+ patterns propagating along the process were investigated, depending on the internal structure of the process, its geometry, and the steady state concentration of inositol 1,4,5-triphosphate molecules.
Izvestiya VUZ. Applied Nonlinear Dynamics. 2025;33(1):82-99
82-99
Comparative analysis of transfer learning performance on generalised EEG data for use in a depression diagnosis task
摘要
The purpose of this work was to analyse the performance of different deep learning methods in the task of depression diagnosis based on bioelectrical brain activity data. In particular, to study the potential of transfer learning using an artificial neural network trained on a significant amount of “generalised” electroencephalography data in the task of diagnosing depression from non-invasive electroencephalogram signals. Methods. Deep learning approaches such as transfer learning and contrastive learning were used in the present study. Artificial neural networks were trained on the public HBN EO/EC task dataset containing recordings of electroencephalogram signals. The 1D CNN and EEGNet architectures were used as auxiliary artificial networks for transfer learning. In order to test the quality of contrastive learning, the dataset was augmented and the following algorithms were selected as the donor network: SimCLR, MoCo, NNCLR, BarlowTwins, DINO. Results. It was found that the EEGNet architecture used as a auxiliary network, due to its small size, does not give the full potential of contrastive learning algorithms. Therefore, EEGNet was replaced by a 1D CNN architecture with a larger number of parameters, which led to an increase in the quality performance of the models. Conclusion. Although the considered method of transient learning looks promising, the specificity of electroencephalogram signals and problems solved on their basis requires large-scale adaptation of algorithms and contrastive optimisation techniques for effective training of the target task. It is also worth noting the crucial role of the representativeness of the data set for training the donor network, since it is the completeness of real observations that increases the effectiveness of augmentation, which leads to an increase in the number of “useful” features in the latent space of the network and the best conditions for transfer learning in the target task. If we talk about the diagnosis of depression, the data should maximally represent examples of electroencephalograms of depressed patients.
Izvestiya VUZ. Applied Nonlinear Dynamics. 2025;33(1):100-122
100-122
Karhunen–Loeve orthogonal decomposition method for problems of EEG assessment of patients with migraine
摘要
The purpose of this work is to identify patterns in the recordings of electroencephalograms of patients with migraine using the Karhunen–Loeve orthogonal decomposition method. The work examines the main features of electroencephalographic dynamics, and the impact on these features of сhronic migraine severity. Methods. To collect experimental data, the method of recording electroencephalograms during the modified multiple sleep latency test was used. During the experiment, studies were conducted of the subjects´reaction to the presented visual stimulus. The obtained data were processed using the Karhunen–Loeve transformation, which allows one to interpret the complex dynamics of the system from the point of view of the coexistence and interaction of coherent orthogonal space-time structures. Results. Studies have shown that the energy distribution of modes in active and sleep states can differ significantly. The character of this distribution depends on the brain zone of signal recordings, on the duration of the experiment, and on at what time point in the experiment certain stages of the subject’s reaction were recorded. It has been shown that the greatest response in the form of evoked potentials in people with migraine is most often localized in the occipital lobe of the brain, and there is a correlation of this effect with the frequency of migraine attacks. For some groups of patients, there is a connection between the severity of evoked potentials in the brain and the energy of the first, most energetic, Karhunen–Loeve mode. Conclusion. It has been shown that there is a relationship between the number of significant modes and the power of the alpha rhythm in electroencephalography signals, and the spatial localization of this effect in the occipital region of the brain can be traced. For the frontal lobe of the brain, significant differences in the distribution of the first mode were demonstrated, assessed for groups of patients with rare and frequent migraine attacks.
Izvestiya VUZ. Applied Nonlinear Dynamics. 2025;33(1):123-139
123-139