Yuri A. Kuznetsov
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View article: Bifurcation Analysis of Generalized Hopf Bifurcation in Ordinary and Delay Differential Equations
Bifurcation Analysis of Generalized Hopf Bifurcation in Ordinary and Delay Differential Equations Open
The generalized Hopf (Bautin) bifurcation is a well-studied codimension two bifurcation characterized by an equilibrium with a pair of simple purely imaginary eigenvalues as the only critical eigenvalues and the vanishing first Lyapunov co…
View article: Numerical Periodic Normalization at Codim 1 Bifurcations of Limit Cycles in DDEs
Numerical Periodic Normalization at Codim 1 Bifurcations of Limit Cycles in DDEs Open
Recent work in [53, 54] by the authors on periodic center manifolds and normal forms for bifurcations of limit cycles in delay differential equations (DDEs) motivates the derivation of explicit computational formulas for the critical norma…
View article: Frontmatter
Frontmatter Open
MATHEMATICAL MODELLING provides English translations of selected new original Russian papers on the theoretical aspects of numerical analysis and the application of mathematical methods to simulation and modelling.The members of the editor…
View article: Subnanosecond Electromagnetic Pulse Generated by a Long Spark Discharge: Lightning Implication
Subnanosecond Electromagnetic Pulse Generated by a Long Spark Discharge: Lightning Implication Open
The effects of generating pulsed radiation by a long spark discharge are important for the development of lightning models and applications related to lightning protection. In experiments with a Marx generator simulating a lightning discha…
View article: Frontmatter
Frontmatter Open
MATHEMATICAL MODELLING provides English translations of selected new original Russian papers on the theoretical aspects of numerical analysis and the application of mathematical methods to simulation and modelling.The members of the editor…
View article: Periodic Center Manifolds for Nonhyperbolic Limit Cycles in ODEs
Periodic Center Manifolds for Nonhyperbolic Limit Cycles in ODEs Open
In this paper, we deal with a classical object, namely, a nonhyperbolic limit cycle in a system of smooth autonomous ordinary differential equations. While the existence of a center manifold near such a cycle was assumed in several studies…
View article: AUTOMATION OF CARGO TRANSPORTATION WITH THE HELP OF INFORMATION PROGRAMS
AUTOMATION OF CARGO TRANSPORTATION WITH THE HELP OF INFORMATION PROGRAMS Open
The criterion for the optimality of the transport process is a minimum of downtime and a maximum of mileage utilization. The purpose of routing is to determine the routes of cargo transportation, ensuring full fulfillment of the task in te…
View article: Periodic Center Manifolds for Nonhyperbolic Limit Cycles in ODEs
Periodic Center Manifolds for Nonhyperbolic Limit Cycles in ODEs Open
In this paper, we deal with a classical object, namely, a nonhyperbolic limit cycle in a system of smooth autonomous ordinary differential equations. While the existence of a center manifold near such a cycle was assumed in several studies…
View article: Periodic Normal Forms for Bifurcations of Limit Cycles in DDEs
Periodic Normal Forms for Bifurcations of Limit Cycles in DDEs Open
A recent work by the authors on the existence of a periodic smooth finite-dimensional center manifold near a nonhyperbolic cycle in delay differential equations motivates the derivation of periodic normal forms. In this paper, we prove the…
View article: Bifurcations of Neural Fields on the Sphere
Bifurcations of Neural Fields on the Sphere Open
A common model to study pattern formation in large groups of neurons is the neural field. We investigate a neural field with excitatory and inhibitory neurons, like Wilson and Cowan (1972), with transmission delays and gap junctions. We bu…
View article: Amplitude–Temporal and Spectral Characteristics of Pulsed UHF-SHF Radiation of a High-Voltage Streamer Discharge in Air under the Atmospheric Pressure
Amplitude–Temporal and Spectral Characteristics of Pulsed UHF-SHF Radiation of a High-Voltage Streamer Discharge in Air under the Atmospheric Pressure Open
A special experimental setup with a three-electrode discharge gap was used to study the dynamic characteristics of the ultra-high- and super-high-frequency (UHF-SHF) electromagnetic radiation of a high-voltage discharge having the streamer…
View article: Bifurcation analysis of Bogdanov-Takens bifurcations in delay differential equations
Bifurcation analysis of Bogdanov-Takens bifurcations in delay differential equations Open
In this paper, we will perform the parameter-dependent center manifold reduction near the generic and transcritical codimension two Bogdanov-Takens bifurcation in classical delay differential equations (DDEs). Using a generalization of the…
View article: Periodic Center Manifolds for DDEs in the Light of Suns and Stars
Periodic Center Manifolds for DDEs in the Light of Suns and Stars Open
In this paper we prove the existence of a periodic smooth finite-dimensional center manifold near a nonhyperbolic cycle in classical delay differential equations by using the Lyapunov-Perron method. The results are based on the rigorous fu…
View article: High-fidelity tracking of the evolution of multilevel quantum states
High-fidelity tracking of the evolution of multilevel quantum states Open
The method of quantum tomography, which allows us to track with high accuracy the evolution of multilevel quantum systems (qudits) in Hilbert spaces of various dimensions is presented. The developed algorithms for quantum control are based…
View article: CALCULATION OF ELECTRONIC STRUCTURE OF 2D NaAu INTERMETALLIC LAYERS
CALCULATION OF ELECTRONIC STRUCTURE OF 2D NaAu INTERMETALLIC LAYERS Open
Проведен расчет плотности состояний различной толщины 2D -слоев интерметаллида NaAu. 2D -слоев интерметаллида NaAu моделировались суперячейки NaAu (111) 2 х 2 х 2. Для монослойного 2D -слоя интерметаллида NaAu установлено наличие запрещенн…
View article: Interplay between normal forms and center manifold reduction for homoclinic predictors near Bogdanov-Takens bifurcation
Interplay between normal forms and center manifold reduction for homoclinic predictors near Bogdanov-Takens bifurcation Open
This paper provides for the first time correct third-order homoclinic predictors in $n$-dimensional ODEs near a generic Bogdanov-Takens bifurcation point. To achieve this, higher-order time approximations to the nonlinear time transformati…
View article: Bifurcations of Heteroclinic Contours in Two-Parameter Planar Systems: Overview and Explicit Examples
Bifurcations of Heteroclinic Contours in Two-Parameter Planar Systems: Overview and Explicit Examples Open
Smooth planar vector fields containing two hyperbolic saddles may possess contours formed by heteroclinic connections between these saddles. We present an overview of known results on bifurcations of these contours. Additionally, two new e…
View article: Frontmatter
Frontmatter Open
Russian JouRnal of numeRical analysis and mathematical modelling provides English translations of selected new original Russian papers on the theoretical aspects of numerical analysis and the application of mathematical methods to simulati…
View article: ELECTRON-STIMULATED DESORPTION OF POTASSIUM ATOMS ADSORBED ON THE SURFACE OF GOLD
ELECTRON-STIMULATED DESORPTION OF POTASSIUM ATOMS ADSORBED ON THE SURFACE OF GOLD Open
Создан ультратонкий слой интерметаллида KAu при комнатной температуре при напылении атомов калия на слой адсорбированного золота на поверхности вольфрама. Исследованы процессы электронно-стимулированной десорбции атомов K с поверхности KAu…
View article: Neural field models with transmission delays and diffusion
Neural field models with transmission delays and diffusion Open
View article: Electron-stimulated desorption of potassium atoms from a potassium layer adsorbed on a tungsten covered with a gold film
Electron-stimulated desorption of potassium atoms from a potassium layer adsorbed on a tungsten covered with a gold film Open
For the first time, electron-stimulated desorption (ESD) of K atoms from the K layer adsorbed on W covered with an Au film was detected and recorded, and the ESD yield was measured by a direct method depending on the electron energy, conce…
View article: Ideologemes in the Russian Vernacular of Muscovite Rus in the 16th-17th Centuries as a Reflection of Inter-Ethnic Interaction
Ideologemes in the Russian Vernacular of Muscovite Rus in the 16th-17th Centuries as a Reflection of Inter-Ethnic Interaction Open
Е.И. Зиновьева, Ю
View article: Precise tomography of optical polarisation qubits under conditions of chromatic aberration of quantum transformations
Precise tomography of optical polarisation qubits under conditions of chromatic aberration of quantum transformations Open
In this work we present an algorithm of building an adequate model of\npolarizing quantum state measurement. This model takes into account chromatic\naberration of the basis change transformation caused by the parasitic\ndispersion of the …
View article: Frontmatter
Frontmatter Open
Russian JouRnal of numeRical analysis and mathematical modelling provides English translations of selected new original Russian papers on the theoretical aspects of numerical analysis and the application of mathematical methods to simulati…
View article: Switching to Nonhyperbolic Cycles from Codimension Two Bifurcations of Equilibria of Delay Differential Equations
Switching to Nonhyperbolic Cycles from Codimension Two Bifurcations of Equilibria of Delay Differential Equations Open
In this paper we perform the parameter-dependent center manifold reduction near the generalized Hopf (Bautin), fold-Hopf, Hopf-Hopf and transcritical-Hopf bifurcations in delay differential equations (DDEs). This allows us to initialize th…
View article: A bifurcation approach to bistability and stabilization in human visual perception
A bifurcation approach to bistability and stabilization in human visual perception Open
We discuss a computational model that describes the stabilization of percept choices under intermittent viewing of an ambiguous visual stimulus at long stimulus intervals (Toff). Unlike previous studies we incorporate the time that the sti…
View article: Frontmatter
Frontmatter Open
Russian JouRnal of numeRical analysis and mathematical modelling provides English translations of selected new original Russian papers on the theoretical aspects of numerical analysis and the application of mathematical methods to simulati…
View article: Development of the Probiotic Feed Supplement Based on Lactobacillus Plantarum to Increase the Broiler Productivity
Development of the Probiotic Feed Supplement Based on Lactobacillus Plantarum to Increase the Broiler Productivity Open
This article reflects the results of the development of a method for testing a promising feed supplement based on the Lactobacillus plantarum strain, with a high antagonistic activity to campylobacter. To determine the digestibility and us…
View article: Technology Development to Suppress the Campylobacter Jejuni in Intestinal Microflora of The Broilers by Lactobacilli
Technology Development to Suppress the Campylobacter Jejuni in Intestinal Microflora of The Broilers by Lactobacilli Open
This article presents a method for determining the microflora of the blind processes of the intestines of broiler chickens receiving heterologous lactobacilli with anti-C.jejuni activity as a feed additive in comparison with intact chicken…
View article: Selection of Promising Lactobacilli Antagonistic to Campylobacter Jejuni
Selection of Promising Lactobacilli Antagonistic to Campylobacter Jejuni Open
This article reflects the results of a study on the selection of promising lactobacilli antagonistic to Campilobacter jejuni, a strain that is the most common and more pathogenic for humans, carried out as part of a project to scientifical…