Izvestiya VUZ. Applied Nonlinear Dynamics

The purpose of this work is to investigate the effect of stochastic perturbations of the white noise type on the stability of capture into autoresonance in oscillating systems with a variable pumping amplitude and frequency such that a center–saddle bifurcation occurs in the corresponding limiting autonomous system. The another purpose is determine the dependence of the intervals of stochastic stability of the autoresonance on the noise intensity. Methods. The existence of autoresonant regimes with increasing amplitude is proved by constructing and justificating asymptotic solutions in the form of power series with constant coefficients. The stability of solutions in terms of probability with respect to noise is substantiated using stochastic Lyapunov functions. Results. The conditions are described under which the autoresonant regime is preserved and disappears when the parameters pass through bifurcation values. The dependence of the intervals of stochastic stability of autoresonance on the degree of damping of the noise intensity is found. It is shown that more stringent restrictions are required to preserve the stability of solutions for the bifurcation values of the parameters. Conclusion. At the level of differential equations describing capture into autoresonance, the effect of damped stochastic perturbations on the center–saddle bifurcation is studied. The results obtained indicate the possibility of using damped oscillating perturbations for stable control of nonlinear systems.

The purpose of this study is to propose an efficient numerical method for solving the inverse nonlinear problem of the movement of the compressor rotor collar in a fluid film thrust bearing. Methods. A periodic thermoelastohydrodynamic (PTEHD) mathematical model of hydrodynamic and thermal processes in a bearing is constructed under the condition of the rotor collar motion. Within the framework of the model, an inverse nonlinear problem of determining the position of the collar under a given external load is formulated. An iterative solution method is proposed, which utilizes the solution of the direct problem. To reduce computational costs, a modified Dekker–Brent method is employed in conjunction with a modified Newton’s method. Results. Numerical experiments have been conducted, demonstrating the effectiveness of the proposed approaches. The suggested methods significantly reduce the required computational resources by minimizing the number of calls to the target function in the optimization problem. A software suite has been developed that allows for the calculation of the nonlinear system of rotor motion under various physical and geometric parameters. Conclusion. An efficient set of numerical methods for solving the inverse nonlinear problem of the motion of the rotor collar in the compressor fluid film thrust bearing is proposed. The method’s effectiveness lies in substantial savings of computational resources. The method’s efficiency has been demonstrated in numerical experiments.

The purpose of this work is to determine the possibility of detecting changes in the relationships between such physiological rhythms as the activity of neurons in the reticular formation of the medulla oblongata, fluctuations in the blood pressure and respiration in anesthetized rats before and during the development of a pathological state associated with painful colorectal distension. This stretch mimics the pain localized in the lower abdomen in patients with irritable bowel syndrome and it is accompanied by responses of the brain neurons, fluctuations in the blood pressure and respiration. The analysis of changes in the relationships of these rhythms consisted in identifying phase synchronization between the time series of the variability of neuronal activity intervals and the variability of blood pressure intervals at the respiratory rate before and during pain exposure. Methods. To solve this problem, the synchrosqueezed wavelet transform method was applied, which makes it possible to effectively calculate the instantaneous frequencies and phases of non-stationary signals. As indicators of synchronization, we used the values of the index and the duration of phase synchronization as a time interval during which the value of the synchronization index is close to 1. Results. It has been established that the pain effect provides an adjustment of the frequency of the neuronal activity variability and the occurrence of synchronization between this activity and the blood pressure variability at the respiratory rate or causes an adjustment of the frequency of the blood pressure variability and the occurrence of synchronization between the blood pressure variability and the respiratory rhythm. It was found that the pain effect increases the duration of phase synchronization between the variability of the blood pressure and the respiratory rhythm or reduces the duration of phase synchronization between the variability of neuronal activity and the respiratory rhythm. Conclusion. The effect of painful colorectal distension on changes in the parameters of phase synchronization between physiological rhythms in anesthetized rats was studied in detail.

Purpose. Studying the possibility of implementing a data classification method based on a spiking neural network, which has a low number of connections and is trained based on local plasticity rules, such as Spike-Timing-Dependent Plasticity. Methods. As the basic architecture of a spiking neural network we use a network included an input layer and layers of excitatory and inhibitory spiking neurons (Leaky Integrate and Fire). Various options for organizing connections in the selected neural network are explored. We have proposed a method for organizing connectivity between layers of neurons, in which synaptic connections are formed with a certain probability, calculated on the basis of the spatial arrangement of neurons in the layers. In this case, a limited area of connectivity leads to a higher sparseness of connections in the overall network. We use frequency-based coding of data into spike trains, and logistic regression is used for decoding. Results. As a result, based on the proposed method of organizing connections, a set of spiking neural network architectures with different connectivity coefficients for different layers of the original network was implemented. A study of the resulting spiking network architectures was carried out using the Free Spoken Digits dataset, consisting of 3000 audio recordings corresponding to 10 classes of digits from 0 to 9. Conclusion. It is shown that the proposed method of organizing connections for the selected spiking neural network allows reducing the number of connections by up to 60% compared to a fully connected architecture. At the same time, the accuracy of solving the classification problem does not deteriorate and is 0.92...0.95 according to the F1 metric. This matches the accuracy of standard support vector machine, k-nearest neighbor, and random forest classifiers. The source code for this article is publicly available: https://github.com/sag111/Sparse-WTA-SNN.

This study is a continuation of M. M. Preobrazhenskaya’s work “Relay System of Differential Equations with Delay as a Perceptron Model”, which aimed to combine approaches related to artificial neural networks and modeling biological neurons using differential equations with delay. The model of a single neuron was proposed, which allows for the existence of special modes called “aging” and “dying” behavior of the neuron. The study found a certain range of parameters where the “dying” mode of the neuron exists and numerically demonstrated the existence of the “aging” mode. Purpose. We will unify the concepts of “aging” and “dying” neurons into the term “freezing” neuron. For this neuron, we will analytically construct a solution and find the range of parameters for its existence and stability, which will extend the results of the reference article. Methods. To study this model, an auxiliary equation obtained by exponential substitution in the original equation is considered. Then, the method of step integration of a differential equation with delay and the introduction of additional functions are used. Results. A solution of the “freezing” neuron type for the original model is constructed, and the range of parameters for the existence and stability of this solution is described. Conclusion. The study obtained an extension of results for solutions of a special type in the model proposed by M. M. Preobrazhenskaya.