Том 32, № 5 (2024)
Editorial
On the anniversary of Professor Alexander Hramov
Аннотация
September 20, 2024 marks the 50th anniversary of Doctor of Physical and Mathematical Sciences, Professor Alexander Evgenievich Khramov, a brilliant scientist, a recognized specialist in the field of radiophysics, nonlinear dynamics and theory of complex networks, biophysics, neuroscience, artificial intelligence and its applications in data analysis and biomedicine.
Izvestiya VUZ. Applied Nonlinear Dynamics. 2024;32(5):567-573
567-573
Applied problems of nonlinear oscillation and wave theory
Synchronization of oscillators with hard excitation coupled with delay Part 2. Amplitude-phase approximation
Аннотация
Aim of this work is to develop the theory of mutual synchronization of two oscillators with hard excitation associated with a delay. Taking into account the delay of a coupling signal is necessary, in particular, when analyzing synchronization at microwave frequencies, when the distance between the oscillators is large compared to the wavelength. Methods. A bifurcation analysis of the mutual synchronization of two generators with hard excitation in the amplitude-phase approximation is carried out. The results of the bifurcation analysis are compared with the results of numerical simulation of the system of differential equations with delay. Results. A complete bifurcation pattern of mutual synchronization on the plane “frequency mismatch — coupling parameter” is presented. In the case of small mismatch and weak coupling, the fixed points, which correspond to modes with dominance of one of the oscillators, merge with saddle fixed points and disappear when the coupling parameter increases. In the case of large mismatch, one of these points either vanishes or loses stability as a result of a subcritical Andronov–Hopf bifurcation. The other of these points remains stable at any values of the coupling parameter, and the oscillation amplitudes of both oscillators gradually equalize and the phase difference tends to zero, i.e., the oscillation mode with dominance of one of the oscillators gradually transforms into the in-phase synchronization mode. It has been found that with an increase in the coupling parameter, a transformation of the basin of attraction of a stable zero fixed point occurs. As a result of this transformation, if at the initial moment of time the oscillations of the generators are close to antiphase, the oscillations decay at any initial amplitudes. Conclusion. The synchronization pattern in the system of delay-coupled oscillators with hard excitation has been studied. It was discovered that in addition to mutual synchronization modes with approximately equal oscillation amplitudes, stationary modes with suppression of oscillations of one generator by another are also possible. The bifurcation mechanisms of the appearance and disappearance of multistability in the system have been examined.
Izvestiya VUZ. Applied Nonlinear Dynamics. 2024;32(5):574-588
574-588
Nonlinear dynamics and neuroscience
A spiking binary neuron — detector of causal links
Аннотация
Purpose. Causal relationship recognition is a fundamental operation in neural networks aimed at learning behavior, action planning, and inferring external world dynamics. This operation is particularly crucial for reinforcement learning (RL). In the context of spiking neural networks (SNNs), events are represented as spikes emitted by network neurons or input nodes. Detecting causal relationships within these events is essential for effective RL implementation. Methods. This research paper presents a novel approach to realize causal relationship recognition using a simple spiking binary neuron. The proposed method leverages specially designed synaptic plasticity rules, which are both straightforward and efficient. Notably, our approach accounts for the temporal aspects of detected causal links and accommodates the representation of spiking signals as single spikes or tight spike sequences (bursts), as observed in biological brains. Furthermore, this study places a strong emphasis on the hardware-friendliness of the proposed models, ensuring their efficient implementation on modern and future neuroprocessors. Results. Being compared with precise machine learning techniques, such as decision tree algorithms and convolutional neural networks, our neuron demonstrates satisfactory accuracy despite its simplicity. Conclusion. We introduce a multi-neuron structure capable of operating in more complex environments with enhanced accuracy, making it a promising candidate for the advancement of RL applications in SNNs.
Izvestiya VUZ. Applied Nonlinear Dynamics. 2024;32(5):589-605
589-605
Biomorphic navigation system version
Аннотация
The purpose of this work is to create and study the dynamics of the functioning of a biorelevant visual navigation system. Methods. The work uses simultaneous navigation and mapping systems RatSLAM and Orb-SLAM. The RatSLAM system is a biorelevant model of visual navigation in the rodent hippocampus. The Orb-SLAM system is a simultaneous navigation and mapping system that works on the principle of searching and tracking changes in the position of key points in the image. Results. The article presents a version of a modified visual navigation system. The system consists of a visual odometry module based on the Orb-SLAM system, as well as a mapping and loop closure module based on the RatSLAM system. This allows you to combine the localization accuracy of systems operating on the principle of tracking key points in the image and neural filtering of biorelevant systems. Using the constructed system, location estimates were obtained on public and new data sets. Conclusion. The constructed visual navigation system determines the location of the subject (video camera) in space, which is in good agreement with the ground truth location data.
Izvestiya VUZ. Applied Nonlinear Dynamics. 2024;32(5):606-624
606-624
The new approach to calculation of physiological cost of activity: antinociception and normalization of the respiratory pattern of heart rate variability
Аннотация
Purpose of this work is to propose an approach to the assessment of allostatic load based on the antinociceptive effect, which appears, obviously, due to changes in the activity of the endogenous opioid system (EOS); to compare the estimates obtained by measuring the pain threshold and calculating the index of respiratory effects on heart rate variability (HRV). The method of measuring the pain threshold is based on fixing the latent time of the thermonociceptive reaction (LTTR). The respiratory effect is measured by graphically determining the minimum normalized power of the fast HRV component in the range of 0.16...0.67 Hz, corresponding to the frequency of the respiratory pattern. Results. Based on small-volume experimental data (4 athletes and 4 episodes of physical activity), a quadratic two-factor regression equation was calculated for LTTR, respiratory effects factor and stress. A high correlation was demonstrated between the respiratory effect on HRV and the LTTR for one studied athlete. Conclusion. Using the example of sports, it is shown that it is possible to track the physiological cost of activities through LTTR. The inconveniences and subjectivity of the LTTR measurement procedure can be circumvented by replacing it with a normalized numerical index that considers the effect of breathing on HRV and the stress index. The proposed approach demonstrates the presence of reference values in the studied group, but requires further specially planned clinical studies.
Izvestiya VUZ. Applied Nonlinear Dynamics. 2024;32(5):625-635
625-635
Searching the structure of couplings in a chaotic maps ensemble by means of neural networks
Аннотация
The purpose of this work is development and research of an algorithm for determining the structure of couplings of an ensemble of chaotic self-oscillating systems. The method is based on the determination of causality by Granger and the use of direct propagation artificial neural networks trained with regularization. Results. We have considered a method for recognition structure of couplings of a network of chaotic maps based on the Granger causality principle and artificial neural networks approach. The algorithm demonstrates its efficiency on the example of small ensembles of maps with diffusion couplings. In addition to determining the network topology, it can be used to estimate the magnitue of the couplings. Accuracy of the method essencially depends on the observed oscillatory regime. It effectively works only in the case of homogeneous space-time chaos. Discussion. Although the method has shown its effectiveness for simple mathematical models, its applicability for real systems depends on a number of factors, such as sensitivity to noise, to possible distortion of the waveforms, the presence of crosstalks and external noise etc. These questions require additional research.
Izvestiya VUZ. Applied Nonlinear Dynamics. 2024;32(5):636-653
636-653
Discrete traveling waves in a relay system of differential-difference equations modeling a fully connected network of synaptically connected neurons
Аннотация
Purpose. Consider a system of differential equations with delay, which models a fully connected chain of m + 1 neurons with delayed synoptic communication. For this fully connected system, construct periodic solutions in the form of discrete traveling waves. This means that all components are represented by the same periodic function u(t) with a shift that is a multiple of some parameter Δ (to be found). Methods. To search for the described solutions, in this work we move from the original system to an equation for an unknown function u(t), containing m ordered delays, differing with step Δ. It performs an exponential substitution (typical of equations of the Volterra type) in order to obtain a relay equation of a special form. Results. For the resulting equation, a parameter range is found in which it is possible to construct a periodic solution with period T depending on the parameter Δ. For the found period formula T = T(Δ), it is possible to prove the solvability of the period equation, that is, to prove the existence of non-zero parameters — integer p and real Δ — satisfying the equation (m + 1)Δ = pT(∆). The constructed function u(t) has a bursting effect. This means that u(t) has a period of n high spikes, followed by a period of low values. Conclusion. The existence of a suitable parameter Δ ensures the existence of a periodic solution in the form of a discrete traveling wave for the original system. Due to the choice of permutation, the coexistence of (m + 1)! periodic solutions is ensured.
Izvestiya VUZ. Applied Nonlinear Dynamics. 2024;32(5):654-669
654-669
Regulation of burst dynamics in the neuron-glial network with synaptic plasticity
Аннотация
The purpose of this study is to develop and investigate a model of astrocytic regulation of burst dynamics of a spiking neural network with synaptic plasticity in inhibitory synapses. Methods. The “integrate and firing” model was used as a neuron model. To describe the dynamics of synaptic connections, a conductance-dependent synapse model with corresponding characteristic relaxation times for excitatory and inhibitory synapses was used. At the same time, inhibitory synaptic plasticity, described by the Vogel model, was used in the dynamics of inhibitory synapses between excitatory and inhibitory neurons. At the same time, the dynamics of excitatory synapses was regulated by the mean-field model of gliotransmitter concentration. Results. A model for the regulation of burst dynamics in a neuron-glial network with inhibitory synaptic plasticity was developed and studied. The main dynamic modes of neuronal activity were obtained in the absence of regulation, in the presence of only synaptic plasticity, and in the presence of also astrocytic regulation of synaptic transmission. A study was conducted of the influence of astrocytic modulation on the frequency of burst activity of the neural network. Conclusion. The study showed the possibility of controlling the burst activity of a spiking neural network by taking into account inhibitory synaptic plasticity for inhibitory synapses between inhibitory and excitatory neurons, as well as astrocytic modulation of excitatory synapses. Astrocytic modulation of synaptic transmission may act as an additional mechanism for maintaining homeostasis in the neural network beyond synaptic transmission, which exists on a faster time scale.
Izvestiya VUZ. Applied Nonlinear Dynamics. 2024;32(5):670-690
670-690
Modeling of global processes. Nonlinear dynamics and humanities
Modeling language competition in a bilingual community
Аннотация
The purpose of this study — construction and research of a new mathematical model of a bilingual community, which takes into account: the effect of mutual assistance within a group of speakers of the same language, the effect of language acquisition by children of bilingual parents at an early age, different prestige of languages for adults. Methods. A new model is being built that takes into account new effects. The model is studied using classical methods with an unlimited increase in dynamics time. The effect of mutual assistance is compared with the effect of language volatility introduced by Abrams and Strogatti. Based on the observed statistical data, using the regression method, the parameters of some languages of England and Canada are determined: Welsh, Scottish, English, French. A forecast is being made for the further development of dynamics. Results. The effects taken into account in the model are confirmed by the correspondence of the development of language dynamics to the characteristics of the language: large values of the parameters of mutual assistance correspond to such a development of language dynamics in which one language displaces the second; at low values of mutual assistance, languages coexist. To model language dynamics using the new model, real statistical data on language pairs is used: Welsh-English, Scots-English, French-English. A forecast is being made for the further development of dynamics by language. Conclusion. General concepts in language dynamics have been supplemented with new ones — the power of mutual assistance within a group of speakers of the same language. The similarity between the effect of language volatility and the effect of mutual assistance is noted.
Izvestiya VUZ. Applied Nonlinear Dynamics. 2024;32(5):691-708
691-708