卷 31, 编号 2 (2023)
Articles
On the anniversary of Sergei A. Kashchenko
摘要
March 14, 2023 celebrates the 70th anniversary of Sergei Aleksandrovich Kashchenko - an outstanding mathematician, doctor of physical and mathematical sciences, professor.
Izvestiya VUZ. Applied Nonlinear Dynamics. 2023;31(2):125-127
125-127
Representation of exact trajectory solutions for chaotic one-dimensional maps in Schroder form
摘要
Purpose of the article is to illustrate the genesis, meaning and significance of the functional Schroder equation, introduced in the theory of iterations of rational functions, for the theory of deterministic chaos by analytical calculations of exact trajectory solutions, invariant densities and Lyapunov exponents of one-dimensional chaotic maps. We demonstrate the method for solving the functional Schroder equation for various chaotic maps by passing to a topologically conjugate mappings, for which finding the exact trajectory solution is a simpler mathematical procedure. Results of the analytical solution of the Schroder equation for 12 chaotic mappings of various types and the calculation of the corresponding expressions for exact trajectory solutions, invariant densities and Lyapunov exponents are presented. Conclusion is made about the methodological expediency of formulating and solving the Schroder equations by the study of the dynamics of one-dimensional chaotic mappings.
Izvestiya VUZ. Applied Nonlinear Dynamics. 2023;31(2):128-142
128-142
Mechanisms leading to bursting oscillations in the system of predator–prey communities coupled by migrations
摘要
The purpose is to study the periodic regimes of the dynamics for two non-identical predator–prey communities coupled by migrations, associated with the partial synchronization of fluctuations in the abundance of communities. The combination of fluctuations in neighboring sites leads to the regimes that include both fast bursts (bursting oscillations) and slow oscillations (tonic spiking). These types of activity are characterized by a different ratio of synchronous and non-synchronous dynamics of communities in certain periods of time. In this paper, we describe scenarios of the transition between different types of burst activity. These types of dynamics differ from each other not so much in size, shape, and number of spikes in a burst, but in the order of these bursts relative to the slow-fast cycle. Methods. To study the proposed model, we use the bifurcation analysis methods of dynamic systems, as well as geometric methods based on the division of the full system into fast and slow equations (subsystems). Results. We showed that the dynamics of the first subsystem with a slow-fast limit cycle directly determines the dynamics of the second one with burst activity through a smooth dependence of regime on the number of predators and a non-smooth dependence on the number of prey. We constructed the invariant manifolds on which there are parts of dynamics with tonic (slow manifold) and burst (fast manifold) activity of the full system. Conclusion. We described the scenario for bursting with different waveforms, which are determined by the appearance of the fast invariant manifold and the location of its parts relative to the slow-fast cycle. The transitions between different types of burst are accompanied by a change in the oscillation period, the degree of synchronization, and, as a result, the dynamics becomes quasi-periodic when both communities are not synchronous with each other.
Izvestiya VUZ. Applied Nonlinear Dynamics. 2023;31(2):143-169
143-169
About dynamics of publication activity on synchronization
摘要
Purpose of the work is to research of the world science publications dynamics on the synchronization. Methods. The research methods are the statistical methods of data processing. Results. The emphasis in the study of synchronization over the past twenty years has shifted from physical and technical sciences to neuroscience with Asian countries domination.
Izvestiya VUZ. Applied Nonlinear Dynamics. 2023;31(2):170-179
170-179
Integrated information and its application for analysis of brain neuron activity
摘要
Purpose of this review is to consider the possibility to apply the integrated information theory to investigate the brain neural activity. Earlier was shown that the integrated information amount Ф quantifies a degree of a dynamic complexity of a system and able to predict a level of its success defined by classic observable benchmarks. For this reason, a question arises about the application of the integrated information theory to analyse changes in brain spiking activity due the acquisition of new experience. Conclusion. The bases of the integrated information theory and its possible application in neurobiology to investigate the process of new experience acquisition were reviewed. It was shown that the amount of integrated information Ф is a metric which is able to quantify the dynamic complexity of brain neural networks increasing when the new experience is acquired. Methods, enabling the practical calculation of Ф for spiking data, were proposed.
Izvestiya VUZ. Applied Nonlinear Dynamics. 2023;31(2):180-201
180-201
Methodology of the neurophysiological experiments with visual stimuli to assess foreign language proficiency
摘要
Aim of this study is to compare different experimental paradigms and to determine parameters suitable for conducting a neurophysiological experiment with visual stimuli to assess foreign language proficiency and providing further time series analysis of electrical brain activity to reveal specific biomarkers. Methods. This paper explores the possibilities and limitations of various experimental studies using the metaanalysis paradigm. Statistical approaches are used to determine significance of the results. Results. We review the current state of research in the field of experimental works related to visual stimulus presentation and verbal performance acquisition. Generalizations and analytical estimates of the experimental parameters used in the studies are carried out to provide recommendations for future experimental research. Conclusion. In this area of applied research, we have developed experimental design and algorithms for working with multiple data sources. In addition, experimental encephalographic studies have been carried out, that allowed the optimal temporal structure selection.
Izvestiya VUZ. Applied Nonlinear Dynamics. 2023;31(2):202-224
202-224
Influence of parametric instability on spin pumping by dipole-exchange magnetostatic surface waves in YIG–Pt structures
摘要
The purpose of this work is to study the influence of four-magnon (4M) parametric instability on spin pumping by dipole-exchange magnetostatic surface waves (MSSW) with the help of the inverse spin Hall effect (ISHE) in structures based on yttrium-iron garnet (YIG) and platinum (Pt). Methods. The experiments were carried out using the delay line structures based on YIG(900 nm)/Pt(9 nm) where electromotive force (EMF) induced by ISHE demonstrates a growth at the frequencies of the resonant interaction between MSSW and volume exchange modes. The frequency dependencies of the amplitude and phase for the delay line structure and EMF (U(f)) from the platinum layer were studied as a function of the MSSW power. Results. It was shown that the resonant EMF growth at the frequencies of dipole-exchange resonances is caused by the presence of Van Hove singularities in the density of states for spin waves at such frequencies that leads to an increase in the efficiency of electron-magnon scattering at the YIG–Pt interface. A growth in MSSW power beyond the threshold of 4M instability development results in a “smoothing” of resonant particularities in the EMF frequency dependence U(f) that can be explained by decreasing efficiency of spin pumping due to destruction of dipole-exchange resonances and related singularities in the density of states of spin waves. Conclusion. Obtained results may be of interest for the development of highly sensitive spin current detectors, as well as for the implementation of spintronic devices.
Izvestiya VUZ. Applied Nonlinear Dynamics. 2023;31(2):225-242
225-242