System Of Differential Equations Research Articles

A system of ODEs for representing trends of CGM signals

Diabetes Mellitus is a metabolic disorder which may result in severe and potentially fatal complications if not well-treated and monitored. In this study, a quantitative analysis of the data collected using CGM (Continuous Glucose Monitoring) devices from eight subjects with type 2 diabetes in good metabolic control at the University Polyclinic Agostino Gemelli, Catholic University of the Sacred Heart, was carried out. In particular, a system of ordinary differential equations whose state variables are affected by a sequence of stochastic perturbations was proposed and used to extract more informative inferences from the patients’ data. For this work, Matlab and R programs were used to find the most appropriate values of the parameters (according to the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC)) for each patient. Fitting was carried out by Particle Swarm Optimization to minimize the ordinary least squares error between the observed CGM data and the data from the ODE model. Goodness of fit tests were made in order to assess which probability distribution was best suitable for representing the waiting times computed from the model parameters. Finally, both parametric and non-parametric density estimation of the frequency histograms associated with the variability of the glucose elimination rate from blood were conducted and their representative parameters assessed from the data. The results show that the chosen models succeed in capturing most of the glucose fluctuations for almost every patient.

Neural network approach to investigate heat transfer in SWCNTs nanofluid within trapezoidal cavity with varied corrugated rod amplitudes

This article presents Artificial Neural Networks (ANN) for convective heat transfer in a trapezoidal cavity subjected to corrugated heated rod inside it. The LevenbergMarquardt algorithm is utilized to optimize the Neural Networks. The trapezoidal cavity has low-temperature inclined walls and adiabatic upper and lower walls compared to the corrugated heated rod. Single-wall carbon (SWCNTs) nanomaterials are submerged in the base liquid water. The flow of SWCNTs-water is generated due to the temperature gradient in the cavity. The system of dimensional partial differential equations has been formulated for the physical setup under investigation. The dimensional system has been converted into a non-dimensional form using dimensionless variables. Finite element is used for the solutions. The dimensionless functions velocity, temperature, and heat transfer rates are studied against the Rayleigh number (Ra). The outcomes are presented in the form of isotherms, contours, tabular values, and graphs. The data for Artificial Neural Networks (ANN) has been generated by FEM against the Nusselt number. The ANN has been trained for a specific amplitude of the rod and predicted heat transfer against a larger amplitude. The results show good agreement for both training and testing data. The outcomes of analysis reveals that convection caused by temperature gradient is dominant for higher values of the Rayleigh number (Ra). Local Nusselt number has been discussed against different amplitudes, and predicted enhancement for the larger amplitude of the rod.

Numerical Study of the 3D MHD Radiative Flow of Williamson Nanofluid with Variable Characteristics Over a Double Stretching Sheet

The current study investigates the influence of variable thermal conductivity and mass conductivity on 3D MHD. The significance of this study lies in mass diffusion on a three-dimensional Williamson nanofluid fluid flow over a double stretched sheet. When thermal radiation and Hall current is present, the heat transfer process is explored to see how chemical reactions affect heat and mass transmission. Additional phenomena, such as momentum slip and convective boundary conditions, contribute to the model's uniqueness. The problem formulation becomes ordinary differential equations with application of the Von Karman similarity variable. Use of the bvp4c function in yields a numerical solution for the system of differential equations. Using MATLAB’s bvp4c function, a numerical solution to the differential equation system is obtained. A graphic is used to discuss the overall result of several metrics compared to the involved profiles. It is believed that as temperature-dependent thermal conductivity and viscosity increase, so does the temperature field. When the Williamson fluid and magnetic parameters rise, the velocity field decays in the x- and y-axis directions. To support the identified issue, a comparison between the current inquiry and a previously published work is also included.

Stability analysis of dual solutions for nonlinear radiative magnetohydrodynamic flow of [formula omitted] hybrid nanofluid over a nonlinearly shrinking surface

The present work explores the existence and temporal stability of dual solutions with the consequence of nonlinear thermal radiation on hybrid nanofluid flow (including Silver and Titanium dioxide nanoparticles in water) past a permeable shrinking sheet. The analysis also considers the united outcomes of suction/injection, Joule heating, viscous dissipation, and magnetohydrodynamics. Employing realistic assumptions and suitable similarity transformations, the governing nonlinear partial differential equations are formulated and altered into a nonlinear ordinary differential equations system. These equations are then solved numerically using the Lobatto IIIA technique. It is observed that dual solutions can occur within a precise range of the shrinking surface parameter. Analyzing the temporal stability of these dual solutions under small disturbances shows that the upper solution branch is stable and represents a physically realistic solution to the problem. In contrast, the lower solution branch is unstable and not physically realizable. No solution exists beyond the critical λc=−1.3915 for the shrinking parameter. The critical values of shrinking parameter λc=−1.2565,−1.3188, and −1.4161 correspond to volume fractions of hybrid nanofluid with φAg−TiO2 of 2%,4%, and 8%, respectively. No solution exists beyond this critical point. The graphical representation and quantitative explanation demonstrate how various emergent characteristics affect momentum and thermal boundary layer profiles, Nusselt number, and skin friction. The velocity and temperature profile of hybrid nanofluid can be improved by adding a small volume of nanoparticle volume fraction. Thermal boundary layer thickness is amplified by an accumulation in the shrinking parameter, power index of velocity component, thermal radiation parameter, and temperature difference ratio. Sheering stress and heat transfer coefficient improve with adding more nanoparticles in the base fluid for the first solution braches, but opposite effects are found in the second solutions. The contributions of this research are significant both theoretically, in terms of advancing the mathematical modeling of hybrid nanofluid flow with heat transfer in engineering systems, and practically, in terms of applications to engineering cooling systems.

Monoterpenoids isomerization and cyclization processes in Gewürztraminer wines: A kinetic investigation at different pH and temperatures

The evolution of volatile compounds in wine comprises several acid-catalyzed reactions, such as glycosides precursors’ hydrolysis and rearrangements, and significantly contributes to its sensory qualities, even after prolonged aging. The aim of this work was to use a well-defined experimental design and to examine how terpenoids in Gewürztraminer wine change over time when subjected to different temperatures and pH levels over two weeks. A theoretically-based approach was used, involving the definition of a complete system of ordinary differential equations (ODE) with well-established boundary conditions (initial concentration of reactants/products), using Kinetiscope, a kinetic simulation software. The calculated optimal rate constants, based on the experimental curves, produced a comprehensive data set describing the evolution of the terpenoid profile, highlighting the reversible and irreversible interconversion processes. Finding revealed that higher pH and lower temperature conditions are crucial for preserving the important terpenoid compounds that characterize the typicality and exemplarity of Gewürztraminer aroma profile.

SBFEM with perturbation method for solving the Reynolds equation

AbstractRotordynamic simulations with nonlinear hydrodynamic bearing forces require a solution of the Reynolds equation at every time step. As a computationally efficient alternative to the standard numerical methods, a semi‐analytical solution based on the scaled boundary finite element method (SBFEM) was developed recently. Through a discretization of the hydrodynamic pressure (dependent variable) along the circumferential but not the axial coordinate, the partial differential equation is transformed into a system of ordinary differential equations. This system of differential equations is referred to as SBFEM equation and can be solved exactly if the influence of shaft tilting is neglected. In common numerical models, this influence can be taken into account without difficulties, but as far as this semi‐analytical approach is concerned, shaft tilting complicates the equations substantially. Therefore, previous studies on the SBFEM solution of the Reynolds equation were conducted without consideration of this effect. The formulation presented in the work at hand no longer requires this simplification. The terms representing the influence of shaft tilting in the SBFEM equation are handled by the perturbation method. The pressure field is expressed by a series expansion, where the solution of order correlates to the power of a perturbation parameter chosen proportional to the tilting angle. The differential equation governing the solution contains lower‐order solutions on its right‐hand side, implying a recursive computation of the series from lowest to highest order. A universal expression for the general solution is formulated, where only the coefficients and the maximum power of the axial coordinate differ for every . This allows the implementation of a general algorithm with no inherent limitation regarding the maximum order of perturbation. For verification, the pressure fields computed by the proposed method are compared to a numerical reference solution, showing that the series converges to the correct result for the investigated set of parameters.

Numerical study of hybrid nanofluid and thermal transport in sun-powered energy ship within the application of parabolic trough solar collectors

PurposeRecent advancements in technology have led to the exploration of solar-based thermal radiation and nanotechnology in the field of fluid dynamics. Solar energy is captured through sunlight absorption, acting as the primary source of heat. Various solar technologies, such as solar water heating and photovoltaic cells, rely on solar energy for heat generation. This study focuses on investigating heat transfer mechanisms by utilizing a hybrid nanofluid within a parabolic trough solar collector (PTSC) to advance research in solar ship technology. The model incorporates multiple effects that are detailed in the formulation.Design/methodology/approachThe mathematical model is transformed using suitable similarity transformations into a system of higher-order nonlinear differential equations. The model was solved by implementing a numerical procedure based on the Wavelets and Chebyshev wavelet method for simulating the outcome.FindingsThe velocity profile is reduced by Deborah's number and velocity slip parameter. The Ag-EG nanoparticles mixture demonstrates less smooth fluid flow compared to the significantly smoother fluid flow of the Ag-Fe3O4/EG hybrid nanofluids (HNFs). Additionally, the Ag-Ethylene Glycol nanofluids (NFs) exhibit higher radiative performance compared to the Ag-Fe3O4/Ethylene Glycol hybrid nanofluids (HNFs).Practical implicationsAdditionally, the Oldroyd-B hybrid nanofluid demonstrates improved thermal conductivity compared to traditional fluids, making it suitable for use in cooling systems and energy applications in the maritime industry.Originality/valueThe originality of the study lies in the exploration of the thermal transport enhancement in sun-powered energy ships through the incorporation of silver-magnetite hybrid nanoparticles within the heat transfer fluid circulating in parabolic trough solar collectors. This particular aspect has not been thoroughly researched previously. The findings have been validated and provide a highly positive comparison with the research papers.

Comparison of different elastic strain definitions for largely deformed SEI of chemo-mechanically coupled silicon battery particles

Amorphous silicon is a highly promising anode material for next-generation lithium-ion batteries. Large volume changes of the silicon particle have a critical effect on the surrounding solid-electrolyte interphase (SEI) due to repeated fracture and healing during cycling. Based on a thermodynamically consistent chemo-elasto-plastic continuum model we investigate the stress development inside the particle and the SEI. Using the example of a particle with SEI, we apply a higher order finite element method together with a variable-step, variable-order time integration scheme on a nonlinear system of partial differential equations. Starting from a single silicon particle setting, the surrounding SEI is added in a first step with the typically used elastic Green–St-Venant (GSV) strain definition for a purely elastic deformation. For this type of deformation, the definition of the elastic strain is crucial to get reasonable simulation results. In case of the elastic GSV strain, the simulation aborts. We overcome the simulation failure by using the definition of the logarithmic Hencky strain. However, the particle remains unaffected by the elastic strain definitions in the particle domain. Compared to GSV, plastic deformation with the Hencky strain is straightforward to take into account. For the plastic SEI deformation, a rate-independent and a rate-dependent plastic deformation are newly introduced and numerically compared for three half cycles for the example of a radial symmetric particle.

Efficient finite element strategy using enhanced high-order and second-derivative-free variants of Newton's method

In this work, we propose a stable finite element approximation by extending higher-order Newton's method to the multidimensional case for solving nonlinear systems of partial differential equations. This approach relies solely on the evaluation of Jacobian matrices and residuals, eliminating the need for computing higher-order derivatives. Achieving third and fifth-order convergence, it ensures stability and allows for significantly larger time steps compared to explicit methods. We thoroughly address accuracy and convergence, focusing on the singular p-Laplacian problem and the time-dependent lid-driven cavity benchmark. A globalized variant incorporating a continuation technique is employed to effectively handle high Reynolds number regimes. Through two-dimensional and three-dimensional numerical experiments, we demonstrate that the improved cubically convergent variant outperforms others, leading to substantial computational savings, notably halving the computational cost for the lid-driven cavity test at large Reynolds numbers.

A discrete fractional order cournot duopoly game model with relative profit delegation: Stability, bifurcation, chaos, 0-1 testing and control

Due to the memory effect, fractional order dynamical systems provide more realistic results compared with ordinary counterparts. In this study, we consider a Cournot-duopoly game model with relative profit delegation in the sense of Caputo fractional derivative. To describe richer dynamical behavior such as chaos in the model, a discrete dynamical system is needed. As a result of the discretization method based on the use of piecewise constant arguments, we obtain a two dimensional system of difference equations. The stability conditions of all equilibrium points of the discrete dynamical system are given comprehensively. The existence of the flip bifurcation in the system has been demonstrated theoretically. Lyapunov exponents and 0–1 test chaos imply that chaotic structures are formed as a result of this bifurcation. In addition, we present the chaos control technique such as Pyragas method to eliminate chaos in the model. All theoretical results dealing with the stability, bifurcation and chaos in the model are stimulated by numerical simulations.

CoOMBE: A suite of open-source programs for the integration of the optical Bloch equations and Maxwell-Bloch equations

The programs described in this article and distributed with it aim (1) at integrating the optical Bloch equations governing the time evolution of the density matrix representing the quantum state of an atomic system driven by laser or microwave fields, and (2) at integrating the 1D Maxwell-Bloch equations for one or two laser fields co-propagating in an atomic vapour. The rotating wave approximation is assumed. These programs can also be used for more general quantum dynamical systems governed by the Lindblad master equation. They are written in Fortran 90; however, their use does not require any knowledge of Fortran programming. Methods for solving the optical Bloch equations in the rate equations limit, for calculating the steady-state density matrix and for formulating the optical Bloch equations in the weak probe approximation are also described. Program summaryProgram Title: CoOMBECPC Library link to program files:https://doi.org/10.17632/5wsg9d52dk.1Developers' repository link:https://github.com/durham-qlm/CoOMBELicensing provisions: GPLv3Programming language: Fortran 90Nature of problem: The present programs can be used for the following operations: (1) Integrating the optical-Bloch equations within the rotating wave approximation for a multi-state atomic system. At the choice of the user, the calculation will return either the time-dependent density matrix at given times or the density matrix in the long time limit if the system evolves into a steady state in that limit. The calculation can be done with or without averaging over the thermal velocity distribution of the atoms. The number of atomic states which can be included in the calculation is limited only by the CPU time available and possibly by memory requirements. An arbitrarily large number of laser or microwave fields can be included in the calculation if these fields are all CW. This number is currently limited to one or two for fields that are not all CW. The calculation can be done in the weak probe approximation, or in the rate equations approximation, or without assuming either of these two approximations. Calculating refractive indexes, absorption coefficients and complex susceptibilities is also possible. (2) Integrating the 1D Maxwell-Bloch equations in the slowly varying envelope approximation for one or two fields co-propagating in a single-species atomic vapour. Although geared towards the case of atoms interacting with laser fields, this code can also be used for more general quantum systems with similar equations of motion (e.g., molecular systems, spin systems, etc.).Solution method: The Lindblad master equation is expressed as a system of homogeneous first order linear differential equations, which are transformed as required and solved to obtain the density matrix representing the state of the atomic system. A variety of methods are offered to this end. The same approach is also used in the calculation of the polarisation of the medium when integrating the Maxwell-Bloch equations. The latter are integrated over space using predictor-corrector methods. The library includes a general driving program making it possible to use these codes without additional program development. The distribution also includes examples of the use of a container for running these programs without a pre-installed Fortran compiler.

Utilizing fractional derivatives and sensitivity analysis in a random framework: a model-based approach to the investigation of random dynamics of malware spread

In this study, an ordinary-deterministic equation system modeling the spread dynamics of malware under mutation is analyzed with fractional derivatives and random variables. The original model is transformed into a system of fractional-random differential equations (FRDEs) using Caputo fractional derivatives. Normally distributed random variables are defined for the parameters of the original system that are related to the mutations and infections of the nodes in the network. The resulting system of FRDEs is simulated using the predictor-corrector method based fde12 algorithm and the forward fractional Euler method (ffEm) for various values of the model components such as the standard deviations, orders of derivation, and repetition numbers. Additionally, the sensitivity analysis of the original model is investigated in relation to the random nature of the components and the basic reproduction number (R0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$R_{0}$\\end{document}) to underline the correspondence of random dynamics and sensitivity indices. Both the normalized forward sensitivity indices (NFSI) and the standard deviation of R0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$R_{0}$\\end{document} with random components give matching results for analyzing the changes in the spread rate. Theoretical results are backed by the simulation outputs on the numerical characteristics of the fractional-random model for the expected number of infections and mutations, expected timing of the removal of mutations from the network, and measurement of the variability in the results such as the coefficients of variation. Comparison of the results from the original model and the fractional-random model shows that the fractional-random analysis provides a more generalized perspective while facilitating a versatile investigation with ease and can be used on different models as well.

Crossed differential systems of equations and Clunie lemma

We study properties of transcendental meromorphic solutions of crossed complex differential systems of equations. For instance, we study the crossed Riccati differential system $$\displaylines{ f(z)^2=1-g'(z), \cr g(z)^2=1-f'(z), }$$ and the crossed Weierstrass differential system $$\displaylines{ f(z)^3=1-g'(z)^2, \cr g(z)^3=1-f'(z)^2. }$$ In addition, we establish a crossed version of Clunie lemma. For more information see https://ejde.math.txstate.edu/Volumes/2024/52/abstr.html

Numerical study on the behavior of a polymeric MHD nanofluid: entropy optimization and thermal analysis

PurposeAnalyzing and reducing entropy generation is useful for enhancing the thermodynamic performance of engineering systems. This study aims to explore how polymers and nanoparticles in the presence of Lorentz forces influence the fluid behavior and heat transfer characteristics to lessen energy loss and entropy generation.Design/methodology/approachThe dispersion model is initially used to examine the behavior of polymer additives over a magnetized surface. The governing system of partial differential equations (PDEs) is subsequently reduced through the utilization of similarity transformation techniques. Entropy analysis is primarily performed through the implementation of numerical computations on a non-Newtonian polymeric FENE-P model.FindingsThe numerical simulations conducted in the presence of Lorentz forces provide significant insights into the consequences of adding polymers to the base fluid. The findings suggest that such an approach minimizes entropy in the flow region. Through the utilization of polymer-MHD (magnetohydrodynamic) interactions, it is feasible to reduce energy loss and improve the efficiency of the system.Originality/valueThis study’s primary motivation and novelty lie in examining the significance of polymer additives as agents that reduce entropy generation on a magnetic surface. The author looks at how nanofluids affect the development of entropy and the loss of irreversibility. To do this, the author uses the Lorentz force, the Soret effect and the Dufour effect to minimize entropy. The findings contribute to fluid mechanics and thermodynamics by providing valuable insights for engineering systems to increase energy efficiency and conserve resources.

Cell seeding dynamics in a porous scaffold material designed for meniscus tissue regeneration

AbstractWe study the dynamics of a seeding experiment where a fibrous scaffold material is colonized by two types of cell populations. The specific application that we have in mind is related to the idea of meniscus tissue regeneration. In order to support the development of a promising replacement material, we discuss certain rate equations for the densities of human mesenchymal stem cells and chondrocytes and for the production of collagen‐containing extracellular matrix. For qualitative studies, we start with a system of ordinary differential equations and refine then the model to include spatial effects of the underlying nonwoven scaffold structure. Numerical experiments as well as a complete set of parameters for future benchmarking are provided.

A qualitative investigation of a system of third-order difference equations with multiplicative reciprocal terms

In this paper, we study the system of third-order difference equations \begin{equation*} x_{n+1}=a+\frac{a_{1}}{y_{n}}+\frac{a_{2}}{y_{n-1}}+\frac{a_{3}}{y_{n-2}}% ,\quad y_{n+1}=b+\frac{b_{1}}{x_{n}}+\frac{b_{2}}{x_{n-1}}+\frac{b_{3}}{% x_{n-2}},\quad n\in \mathbb{N}_{0}, \end{equation*}% where the parameters $a$, $a_{i}$, $b$, $b_{i}$, $i=1,2,3$, and the initial values $x_{-j}$, $y_{-j}$, $j=0,1,2$, are positive real numbers. We first prove a general convergence theorem. By applying this convergence theorem to the system, we show that positive equilibrium is a global attractor. We also study the local asymptotic stability of the equilibrium and show that it is globally asymptotically stable. Finally, we study the invariant set of solutions.

Could Olympic Gels of Polystyrene be Produced by ARGET ATRP From Bifunctional Initiators?

The kinetics of gelation in the Activators Regenerated by Electron Transfer Atom Transfer Radical Polymerization (ARGET ATRP) of styrene, using a bifunctional initiator and no crosslinking agents are investigated. By applying the method of moments, we develop a system of differential equations that accounts for the formation of polymer rings. The kinetic rate constants of this model are optimized on the experimentally determined kinetics, varying the reaction temperature and ethanol fraction. Subsequently, we explore how variations in the amounts of catalyst, initiator, and reducing agents affect the simulated equilibria of ARGET ATRP, the emergence of gelation, and the swelling properties of the resulting networks. These findings suggest that favoring ring formation enhances the gelation phenomenon, supporting the hypothesis that the networks formed under the reported reaction conditions are olympic gels.

A Cancer Subpopulation Competition Model Reveals Optimal Levels of Immune Response that Minimize Tumor Size.

Breast cancer is a complex disease with significant phenotypic heterogeneity of cells, even within a single breast tumor. Emerging evidence underscores the significance of intratumoral competition, which can serve as a key contributor to cancer drug resistance, imparting substantial clinical implications. Understanding the competitive dynamics is paramount as it can significantly influence disease progression and treatment outcomes. In the present work, a mathematical model was developed using a system of differential equations to describe the dynamic interactions between two cancer subtypes (each further classified into cancer stem cells and tumor cells) and innate immune cells. The purpose of the model is to comprehensively understand the competitive interactions between the heterogeneous subpopulations. The equilibrium points and stability analysis for each equilibrium point were established. Model simulations showed that the competition between two cancer subtypes directly affects the number of both species. When competition between two cancer subtypes is strong, increasing the immune response rate specific to the more competitive species effectively reduces the tumor size. However, if the competition is relatively weak, an optimal immune response rate is required to minimize the total number of tumor cells. Rates below the optimal level fail to reduce the population of the stronger species, whereas rates above the optimal level can lead to the recurrence of the weaker species. Overall, this model provides insights into breast cancer dynamics and guides the development of effective treatment strategies.

On the inverse problem of time dependent coefficient in a time fractional diffusion problem by sinc wavelet collocation method

The object of this study is to establish the unknown function in a time fractional diffusion problem and the solution as well by utilizing Sinc wavelet collocation method (SWCM) and residual power series method (RPSM) together. SWCM enables us to convert time fractional diffusion problem into a system of fractional ordinary differential and algebraic equations. At this stage, the unknown function and the solution are constructed in the series form by employing RPSM. The novelty of this study is that the combination of SWCM and RPSM is utilized to establish the solution of inverse coefficient problem for the first time. Demonstrative examples are presented to articulate the implementation and importance of the proposed method.

The study of forced oscillations in the non-linear system of an individual traction drive

BACKGROUND: The processes taking place in the ‘traction electric drive – wheel – road’ system during acceleration and braking cause increased dynamic loads on drive components, which may lead to a breakdown. Therefore, it is important to control the drive in a way to minimize and to suppress the given processes. To make it possible, the control system is to be equipped with a resistance torque observer at the electric motor shaft. In addition, in any system, there is a heighten interest in study of arise of resonances, which come with abrupt increase of oscillations amplitudes. Therefore, the features of oscillation phenomena in the given non-linear system are to be studied. AIM: Identification of the peculiarities of oscillatory processes, resonance phenomena in the systems of electromechanical drive of vehicles, which are nonlinear technical systems. METHODS: The study of features of the oscillating processes and the study of capabilities of arise of resonant phenomena were conducted using analysis of the differential equations system describing the operation of the non-linear system. RESULTS: The features of the oscillating phenomena in non-linear systems of interaction between an elastic wheel and road as well as capabilities of arise of resonant phenomena were considered. It is defined that arise of the resonant phenomena in the considered systems is not possible due to breakdown of them. The behavior of modes of interaction between an elastic wheel and road during intensive acceleration and braking was analyzed. The abrupt shock behavior of change rate of wheel torque and current consumed by a drive as well as features of lowering of them when using the self-oscillating phenomena suppression were found. CONCLUSION: The practical value of the study lies in ability of using the proposed conclusions at development of units of a traction electric drive and at synthesis of vehicle motion control systems.