ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

# Нелинейная динамика и нейронаука

## Modern Approaches to the Formation of Intelligent Monitoring in the Context of Digital Manufacturing

The purpose of this study is to analyze the problems and approaches to intelligent monitoring in multiproduct automated production with regard to its digitalization; examine an example of the manufactured part quality monitoring based on neural networks. Methods. The paper investigates the possibility of using artificial neural networks to monitor the quality of manufactured parts in real time. Results.

## Calcium concentration in astrocytes: Emergence of complicated spontaneous oscillations and their cessation

The purpose of this work is to show the mechanisms of transitions between different dynamic modes of spontaneous astrocytic calcium activity. With this aim, dynamics of recently introduced Lavrentovich–Hemkin mathematical model was examined by both analytical and numerical techniques. Methods. In order to obtain the conditions for the oscillations cessation, the linear stability analysis for the equilibrium point was carried out. Complicated dynamics was studied numerically by calculations of time traces and bifurcation diagrams. Results.

## Network activity in primary hippocampal cultures upon HIF-prolyl hydroxylase inhibition

Neural network functional activity study and estimation of activity changes in different pathological states (e.g. in hypoxia conditions) is an important scientific task. Hypoxia is one of key damaging factors of various brain pathologies such as stroke, traumatic brain injury, neurodegenerative disease etc. Hypoxia causes structural and functional destruction of neuron-glial networks. The protein calls hypoxia-inducible factor (HIF) is one of the main endogenous molecular regulators of the cell’s response to hypoxia.

## Recurrence quantification analysis provides the link between age-related decline in motor brain response and complexity of the baseline EEG

The goal of the present study is to investigate the effect of healthy aging on the neuronal mechanisms supporting human brain activity during motor task performance. Such biomarkers of the age-related changes can be detected using mathematical methods of time-series analysis and complexity analysis. Methods. In the present paper, recurrence quantification analysis (RQA) measures are employed to explore the complexity of the pre-movement EEG in young and elderly adult groups.

## Boundaries of computational complexity and optimal cluster’s quantity for controlled swarm in non-cooperative games

The purpose of the work is to determine the relationship between the computational complexity of controlling a swarm of particles and the available computational resources for choosing the optimal control strategy. We find formulas for the relationship between the available computational complexity, the number of clusters in the swarm, the number of interacting players, and the depth of calculations to search the suboptimal control. Methods. To find the optimal control, the method of maximizing the target objective function is used.

## Mathematical model and dynamical analysis of the human equilibrium seeking training

The purpose of this work is to determine the ability of the partial directed coherence method to identify the
directed interaction between nonlinear systems correctly in presence of nonlinear couplings between systems, as well as
in the case when the measured signals are generated by objects of high dimension. The another purpose is to determine
the dependence of the coupling estimation results on the parameters: series length, sampling rate, model dimension and the

## On trajectory tracking control of prismatic and revolute joined robotic manipulators

The purpose of this paper is to construct a trajectory tracking feedback controller for prismatic and revolute joined
multi-link robotic manipulators using a new form of sliding modes. Methods. In this paper, the Lyapunov functions method
has been applied to establish the stability property of the closed-loop system. Results. Due to the presence of rotational joints,
the motion equations of the manipulator are periodic in the angular coordinates of the corresponding links. A control law is

## Control of network bursting discharges by local electrical stimulation in spiking neuron network

Goal. The paper is devoted to controlling the dynamics of spike neural networks by local periodic stimulation of various network sections. Methods. The simulation uses a network of synaptically connected spike neurons distributed in two-dimensional space. The dynamics of the transmembrane potential of neurons is described by the Izhikevich model, short-term synaptic plasticity is represented by the model Tsodyksa–Markram, the effects of changes in the efficiency of connections between neurons are modeled using spike-timing-dependent plasticity (STDP). Results.

## Modern research on primary school children brain functioning in the learning process: Review

The purpose of this article is to review studies related to the study of primary school children’s brain activity in the educational process. In addition, to find out how common such researches are and to define the main directions of scientists’ activities on the topic, and their chosen research approaches. Methods. Qualitative content analysis was used to select articles suitable for the topic under study: several sets of keywords, journals with a quartile of at least the second, and English language publications were identified as requirements. Results.

## Движение тела с возрастающим ускорением свободного падения

Цель исследования – аналитическое описание нормального падения тела на поверхность беатмосферной планеты. При этом движение нормально падающего тела характеризуется возрастающим ускорением свободного падения. Методы. Задача о скорости, времени и ускорении нормального падения тела на поверхность планеты при отсутствии атмосферы сводится к решению дифференциального уравнения второго порядка, которое решается стандартным методом. Особенностью решения является формальное использование табличного интеграла на промежуточном этапе.