Vol 31, No 2 (2023)

March 14, 2023 celebrates the 70th anniversary of Sergei Aleksandrovich Kashchenko - an outstanding mathematician, doctor of physical and mathematical sciences, professor.

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.

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.

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.