Instability Conditions Research Articles

Exploring cooperative hunting dynamics and PRCC analysis: insights from a spatio-temporal mathematical model

The proposed mathematical model explores the intricate dynamics of a predator-prey system involving prey infection and cooperative hunting of predators. The model incorporates habitat complexity, emphasizing its influence on ecological interactions. The well-posedness of the system has rigorously been examined in a temporal setting and also conducted stability analysis. The bifurcation analysis reveals the existence of several local bifurcations on the system, namely transcritical bifurcation, saddle-node bifurcation, and Hopf bifurcation. Furthermore, these investigations delineate the two-dimensional bifurcations including Bogdanov–Takens and cusp bifurcations for different parametric combinations. With suitable choices of parameter values, the proposed model exhibits diverse dynamic phenomena, including bistable and tri-stable behavior. Latin hypercube sampling is utilized to conduct uncertainty analysis on input parameters, aiming to observe their effects on population dynamics. Subsequently, Kendall’s tau and Spearman’s rank correlation coefficients are also computed to investigate the impact of these uncertainties on the population. In the later part, a spatio-temporal system is proposed with two-dimensional diffusion terms to obtain the conditions for Turing instability. Numerical simulations have been conducted to observe the emergence of spatial patterns and the impact of predator cooperation in these patterns. The study provides valuable insights into the dynamics of complex ecological systems, emphasizing the interplay of spatial and temporal factors in shaping population dynamics and predator-prey interactions.

Hopf bifurcation and patterns formation in a diffusive two prey-one predator system with fear in preys and help

Recognizing the relationship between the spatial patterns in species concentrations and ecological heterogeneity is crucial for understanding demographics and species governance in a given domain, as ecological patterning processes are believed to be imitated in real ecosystems. In this present article, we have considered a two-prey-one-predator system with Holling type-II functional response where both the preys have fear of predator and compete in the absence of predator. Additionally, we have assumed that both the prey help each other when the predator attacks them. We have incorporated self-diffusion in this system under Neumann boundary conditions. The existence and stability conditions of different equilibria are discussed. We have studied the Hopf bifurcation around positive offset and derived the stability and direction of periodic solution. We have done a series of numerical simulations to ensure our theoretical finding. Diffusion-driven instability conditions are obtained. Different instability regions and fascinating patterns, such as spots, mixtures, and stripes, are depicted. Spatiotemporal dynamics also reflects that prey populations are located in isolated areas of low population concentration with increasing level of fear, whereas an increase in handling time forms lower-density stripes. But with increasing help, prey becomes more concentrated in some stripe regions. In the Hopf-Turing region, it is observed that the diffusion coefficient of predators can stabilize the system. Overall, pattern creation in predator-prey systems can help anticipate long-term system behaviour and analyze the influence of ecological factors on system dynamics.

Kirigami sheets in fluid flow

Kirigami patterned materials have found several applications in recent years due to their ability to assume complicated shapes and exhibit emergent physical properties when exposed to external forces. Consisting of an array of cuts in a thin material, fabrication of these patterns can be quite simple. Here we show that when they are placed in fluid flow, kirigami cut sheets with various patterns produce a variety of flow patterns in the wake. Through several sets of experiments, we show that kirigami sheets placed in flow can undergo static or dynamic flow-induced instabilities as a result of which they can buckle or undergo limit cycle oscillations, or they can remain stable while undergoing very large elongations. These structural responses produce several different types of fluid patterns in the wake. We show that vortices both at small scales (scales comparable with the size of the individual kirigami cuts) and large scale (scales comparable with the size of the sheet) are formed in the wake of kirigami sheets. We also show that jets of different sizes can be formed and directed passively using kirigami sheets. These results show the potential of kirigami sheets for passive flow control.

Influence of temperature-dependent density inhomogeneity on the stability of atmospheric stratified fluids

The stability of atmospheric stratified fluids is revisited to study the influence of the temperature-dependent density inhomogeneity due to thermal expansion in the Earth’s lower atmosphere (with heights 0 to 50 km) under the action of gravity. Previous theory in the literature [Phys. Lett. A 480 (2023) 128 990] is modified and advanced. It is found that the Brunt-Väisälä frequency associated with internal gravity waves is modified, leading to new instability conditions of vertically stratified fluids. The possibility of the onset of Rayleigh-Bénard convective instability is also discussed, and the influences of the modified Brunt-Väisälä frequency and the density and temperature gradients on the instability growth rates are studied.

On Strain-Hardening Behavior and Ductility of Laser Powder Bed-Fused Ti6Al4V Alloy Heat-Treated above and below the β-Transus.

Laser powder bed-fused Ti6Al4V alloy has numerous applications in biomedical and aerospace industries due to its high strength-to-weight ratio. The brittle α'-martensite laths confer both the highest yield and ultimate tensile strengths; however, they result in low elongation. Several post-process heat treatments must be considered to improve both the ductility behavior and the work-hardening of as-built Ti6Al4V alloy, especially for aerospace applications. The present paper aims to evaluate the work-hardening behavior and the ductility of laser powder bed-fused Ti6Al4V alloy heat-treated below (704 and 740 °C) and above (1050 °C) the β-transus temperature. Microstructural analysis was carried out using an optical microscope, while the work-hardening investigations were based on the fundamentals of mechanical metallurgy. The work-hardening rate of annealed Ti6Al4V samples is higher than that observed in the solution-heat-treated alloy. The recrystallized microstructure indeed shows higher work-hardening capacity and lower dynamic recovery. The Considère criterion demonstrates that all analyzed samples reached necking instability conditions, and uniform elongations (>7.8%) increased with heat-treatment temperatures.

Counteraction of Russian Finance Market Against External Sanctions Pressure

The article shows the impact of external economic sanctions on the Russian financial market. Special attention is paid to the currency, commodity and derivative markets of the Moscow Stock Exchange. The main focus of the work is the analysis of changes in market dynamics and pricing under the influence of political and economic constraints. Methodologically, the study is based on a comprehensive analysis of trade session data, including statistical processing and modeling of market reactions. The use of actual analytical methods made it possible to identify nonlinear dependencies and hidden patterns of behavior of market participants. The results of the study demonstrate that sanctions have had a significant impact on volatility, liquidity and market structure. The authors show the influence of political factors on financial instruments in a crisis, as well as develop new methodological approaches to analyzing financial market data. The results of the work can be used to coordinate trading strategies, develop market regulation policies and assess risks in conditions of political instability. The study also provides a basis for further analysis of the consequences of economic sanctions and the development of strategies to adapt to changing market conditions.

The political crisis of autumn-winter 1993 on the pages of the newspaper "Muromsky Krai"

The article is devoted to the reflection of the political crisis of the end of 1993 in the provincial periodical of Murom, Vladimir region. The author refers to the journalistic articles of the local newspaper "Muromsky Krai" from September 23, when the first information about the events in Moscow was published, to December 23, when the results of the December 12 vote were published in the newspaper. Information about the situation on the ground in conditions of severe crisis and political instability, brought to the peak of tension in the autumn of 1993, is able to tell the mood in society and the position of municipal authorities, as well as reveal the role of the media and journalists, in particular, in localizing and resolving conflicts of interest both within the government and between the government and society at the local level. The research is based on the principles of objectivity and historicism. In addition, historical, systematic and chronological methods allowed us to reveal the question posed to the author about the reflection of the political crisis of the end of 1993 in the Murom newspaper. The source base of the study was the issues of the local socio-political newspaper "Muromsky Krai". To solve the scientific problem, the author applied to the municipal archive of Murom and the local library. The journalists of the local newspaper paid great attention to the political vicissitudes and the participation of citizens in resolving the political confrontation. The author of the study studied this layer of materials in detail and came to the conclusion that urban journalists, with their very peaceful position, contributed to maintaining calm among the Muromites during an extremely difficult period of Russian history. At the same time, citizens, having shown awareness, preferred another way of interacting with the authorities to strikes and mass rallies – participation in the elections on December 12, the results of which showed dissatisfaction with the policy of the central authorities.

Трудовая миграция в российских регионах в контексте обеспечения экономической безопасности

In the accepted understanding of the role of labor migration as a leading factor in ensuring the economic security of Russia and its regions, it is necessary to proceed from the content of migration as a complex, multidimensional phenomenon, characterized by multidirectional and contradictory dynamics of the processes occurring in it. In conditions of geopolitical and macroeconomic instability, the diagnosis of these processes is updated in connection with sharp structural shifts in labor migration and changes in their influence on the economic security of Russian regions and the country. Based on a structural-dynamic analysis made with the use of official statistical information, the dynamics and effectiveness of the processes accompanying labor migration and their impact on the economic security of Russia, its regions, and macro-regions were identified. The main trends in labor migration at the macro level are the predominance of internal migration flows over external ones against the negative increase in labor migrants from countries outside the CIS countries and the reorientation of labor flows to other countries; changes in the sectoral structure of migration; and the high share and growth of illegal migration. At the meso level, there is a high level of differentiation in labor migration flows and, as a result, their ambiguous impact on the economic security of Russian macro-regions and their constituent entities. The main factors hindering the positive impact of labor migration on the economic security of the regions of the Southern Federal District are differences in their sectoral specialization; the state of social infrastructure, education, and healthcare; level of employment; environmental and climatic living conditions; composition and structure of the population; and quality of life. The solution to the problems of labor migration in the Southern Federal District, which can ensure an increase in the migration attractiveness of the territories of the macro-region, lies, first of all, in the growth and balance of the quality of life of the population in the regions of the Southern Federal District, increasing the effectiveness of the state regional industrial and social policy, and strengthening the place and role of migration policy in long-term programs of regional development.

Intensive Radiosonde Observations of Environmental Conditions on the Development of a Mesoscale Convective System in the Baiu Frontal Zone

AbstractMesoscale convective systems (MCSs) that occur in the Baiu frontal zone (BFZ) can cause devastating flash floods during early summer in Japan; however, the environmental conditions necessary for their development require further investigation. High‐frequency atmospheric soundings, conducted using multiple marine vessels in the East China Sea on 19 June 2022, captured the detailed environmental conditions pertaining to the development of an MCS within the BFZ. The MCS, which developed rapidly without any remarkable preceding synoptic or mesoscale disturbance in the mid‐ or upper troposphere, caused intense precipitation exceeding 80 mm/hr. The MCS persisted for approximately 6 hr, and it intensified when the influx of nearly saturated air near the sea surface toward a weak surface front overlapped with the influx of free‐tropospheric moist air. The influx of nearly saturated air near the sea surface ensured conditional instability within the lower troposphere. The influx of moist air in the free troposphere contributed to the near‐saturation conditions above the boundary layer, a feature inherent to the BFZ, and played an important role in minimizing the reduction in the buoyancy of air parcels. The results of this study indicate that a better forecast of the horizontal distribution of free tropospheric moist air is beneficial for limiting the potential area of genesis of MCS in the BFZ, and a more comprehensive understanding of the vertical variations in moisture transport contributes to an improved forecast skill for MCS in the BFZ.

A Radar-Based 10-Year Climatology of Convective Snow Events in Central Pennsylvania

Abstract Convective snow (CS) presents a significant hazard to motorists and is one of the leading causes of weather-related fatalities on Pennsylvania roadways. Thus, understanding environmental factors promoting CS formation and organization is critical for providing relevant and accurate information to those impacted. Prior research has been limited, mainly focusing on frontal CS bands often called “snow squalls”; thus, these studies do not account for the diversity of CS organizational modes that is frequently observed, highlighting a need for a robust climatology of broader CS events. To identify such events, a novel, radar-based CS detection algorithm was developed and applied to WSR-88D radar data from 10 cold seasons in central Pennsylvania, during which 159 cases were identified. Distinct convective organization modes were identified: linear (frontal) snow squalls, single cells, multicells, and streamer bands. Each algorithm-flagged radar scan containing CS was manually classified as one of these modes. Interestingly, the most-studied frontal mode only occurred <5% of the time, whereas multicellular modes dominated CS occurrence. Using the times associated with each CS mode, synoptic and local environmental information from model analyses was investigated. Key characteristics of CS environments compared to null cases include a 500-hPa trough in the vicinity, lower-tropospheric conditional instability, and sufficient moisture. Environments favorable for the different CS modes featured statistically significant differences in the 500-hPa trough axis position, surface-based CAPE, and the unstable layer depth, among others. These results provide insights into forecasting CS mode, explicitly presented in a forecasting decision tree. Significance Statement Convective snow events such as snow squalls are a leading cause of weather-related deaths on Pennsylvania roads. Research into these events is limited, thus negatively impacting forecast skill. To better understand convective snow event frequency of occurrence, inter- and intra-annual variability, and their supporting environments, we performed a 10-yr radar-based climatology of these events. We report the results of this climatology and on the statistically significant differences in their supporting environments. The latter are used to propose a forecasting framework for convective snow, which may improve the predictability of convective snow in an operational setting.

THE ESSENCE, COMPONENTS AND STAGES OF THE DIAGNOSTIC STATE OF THE REGION’S SOCIO-ECONOMIC DEVELOPMENT IN THE CONDITIONS OF MACROECONOMIC INSTABILITY

Objective. The objective of the present article is to study the essence and highlight the main components and stages of diagnosing the state of socio-economic development of the region in conditions of macroeconomic instability. Methods. The following methods were used to conduct the research: the analysis method (to study the essence of the diagnosis of the state of socio-economic development of the region and to determine the components of the diagnosis of the socio-economic development of the region in conditions of macroeconomic instability), the method of formalization (to distinguish the stages of analysis of the development of the region in conditions of macroeconomic instability ) and the graphic method (for constructing a sequence diagram of the diagnosis of socio-economic development of the region). Results. Diagnosis of the socio-economic development of the region is a necessary condition for the development of effective policies and strategies aimed at ensuring sustainable development, increasing competitiveness and improving the quality of life of the population of the region. A comprehensive approach to diagnosing the socio-economic development of the region, which includes detailed analysis, modeling, development and implementation of strategies, is a key element of successful state regulation and ensuring stable development in conditions of macroeconomic instability. In the process of researching the essence and main components of the diagnosis of the state of socio-economic development of the region under conditions of macroeconomic instability, the components of the diagnosis of the socio-economic development of the region under conditions of macroeconomic instability were singled out, a scheme of the sequence of diagnosis of the socio-economic development of the region under conditions of macroeconomic instability was proposed, and the scheme was graphically presented stages of analysis of the region's development in conditions of macroeconomic instabilit

THEORETICAL ASPECTS AND ESSENTIAL DEFINITIONS OF REGIONAL ECONOMY STATE REGULATION IN MACROECONOMIC INSTABILITY CONTEXT

Objective. The objective of the article is to analyze and systematize the theoretical aspects and essential definitions of state regulation of the economy of regions in the context of macroeconomic instability, as well as to determine the basic principles of effective management of regional policy in the context of macroeconomic instability. Methods. The following methods are applied to conduct the research: the analysis method (to study the theoretical aspects and determine the essential definitions of the state regulation of the economy of the regions), the induction method (to highlight the areas of application of methodological approaches to the assessment of the effective management of regional policy in conditions of macroeconomic instability and to define key concepts which are based on scientific approaches to the state regulation of the economy of regions in conditions of macroeconomic instability) and a graphic method (for building a refined scheme of the components of macroeconomic instability of regions and expanding the directions for overcoming them). Results. Macroeconomic instability is characterized by significant fluctuations in key macroeconomic indicators which may be caused by internal and external economic, political, and social factors. Macroeconomic instability affects regional development due to reduced investment, reduced budget revenues, increased unemployment and social tension. In order to achieve socio-economic stability and successful development of the region, state regulation should ensure successful overcoming of macroeconomic instability by forecasting crisis phenomena, preventing them and creating reserves in advance to eliminate their consequences. The key factor is the definition and consideration of all components of macroeconomic instability. The proposed sixth component of regional macroeconomic instability - military instability - requires the development of comprehensive security strategies, including strengthening the country's defense capabilities, providing social and economic support for affected regions as well as active international cooperation for post-war reconstruction, maintaining peace and stability. It is also important to deal with issues of reintegration of the affected territories and population, restoration of infrastructure and economic activity in conflict zones.

Control of an Energy-Harvesting System Using Sinha’s Theory for the Purpose of Energy Production

The goal of this study was to develop a linear feedback control method to increase the energy produced for a parametrically excited energy-harvesting system. The chosen control design uses state feedback based on the Lyapunov–Floquet transformation to direct the system dynamics toward a previously chosen trajectory. The methodology of this work was based on the studies of Sinha and Butcher. They developed stability and control analysis techniques based on Floquet theory and the approximation of the state transition matrix of systems that have periodic coefficients in time. It was observed that the stability and instability conditions of the system were obtained from the choice of physical parameters related to the parametric excitation force. When the control technique was applied to the system, it was found that the suggested control effectively directed the system’s trajectory in the direction of the predetermined trajectory. The application of control significantly increased the energy generation compared with the uncontrolled system, which was seen when comparing the energy generated by the uncontrolled system and the net energy generated by the controlled system.

Nonlinear lattices from the physics of ecosystems: The Lefever–Lejeune nonlinear lattice in ℤ2

We argue that the spatial discretization of the strongly nonlinear Lefever–Lejeune partial differential equation defines a nonlinear lattice that is physically relevant in the context of the nonlinear physics of ecosystems, modelling the dynamics of vegetation densities in dry lands. We study the system in the lattice , which is especially relevant because of its natural dimension for the emergence of pattern formation. Theoretical results identify parametric regimes for the system that distinguish between extinction and potential convergence to nontrivial states. Importantly, we analytically identify conditions for Turing instability, detecting thresholds on the discretization parameter for the manifestation of this mechanism. Numerical simulations reveal the sharpness of the analytical conditions for instability and illustrate the rich potential for pattern formation even in the strongly discrete regime, emphasizing the importance of the interplay between higher dimensionality and discreteness.

Роль креативного менеджменту в оптимізації кадрової політики в умовах нестабільності

This article examines the role of creative management in optimizing personnel policy in conditions of instability. The main aspects of the topic are considered based on the analysis of modern scientific literature and the practical experience of modern scientists in the field of management. It was determined that creative management is aimed at stimulating innovative processes and developing the creative abilities of personnel. It was also summarized that in conditions of economic instability, this approach becomes strategically essential for enterprises, as it allows them to adapt to changes in the internal and external environment. In addition, creative management models were systematized, which helped in the organization of effective personnel management and ensured the sustainable development of the enterprise. It is substantiated that integrating creative management into personnel policy contributes to increasing the motivation of employees, strengthening the corporate culture, and contributing to the innovative development of the organization. The research findings show that creative management is a necessary tool for the successful functioning of an enterprise in conditions of instability. Also, the implementation of creative models contributes to the formation of flexible and competitive personnel capable of quickly responding to changes and achieving the organization’s strategic goals. Creative management plays a vital role in optimizing personnel policy in conditions of instability, providing the ability to effectively respond to challenges and adapt to changes in both the internal and external environment of the functioning of enterprises. Thanks to the creative approach to the management of human resources, there is a qualitative restructuring of the work process aimed at stimulating innovation and developing the creative potential of employees. In addition, this approach creates conditions for generating new ideas that contribute to solving complex problems and support the enterprise’s competitiveness. Keywords: creative management, personnel policy, instability, innovation, staff motivation, organizational culture, strategic goals, competitiveness.

ТИПОЛОГИЯ ИНСТИТУЦИОНАЛЬНЫХ ФАКТОРОВ, ОКАЗЫВАЮЩИХ ВЛИЯНИЕ НА РАЗВИТИЕ ЭКОНОМИКИ СЕВЕРНЫХ РЕГИОНОВ

Institutional factors play a key role in shaping the direction and nature of regional economic development. They define rules and regulations that affect economic activity, the investment climate, and social progress in the regions. The author presents a comprehensive typology of institutional factors determining the socio-economic development of the northern regions. This typology identifies the key institutional factors affecting both the economy and the social sphere of the northern region. The study identifies various types of institutional factors grouped into seven categories, each of which reflects unique approaches to analyzing their impact on regional development. These groups include specific institutional characteristics that determine the characteristics and directions of development of different regions. The research methods included content analysis of domestic and foreign publications, semantic analysis of definitions of institutions, as well as a systematic approach involving the study of phenomena in their constant development and interrelation. This study is important for determining the optimal strategies for the development of institutions that contribute to sustainable economic growth and social progress in the regions. The novelty of the work lies in the proposed author's typology of institutional factors, which comprehensively covers all aspects of their impact on the development of regions. Understanding and analyzing these factors become an important tool for developing an effective strategy for the development of the region in conditions of instability of the national economic system. The application of this typology makes it possible to more accurately identify the weaknesses and strengths of the institutional environment of each region, which, in turn, contributes to the creation of targeted measures to improve the institutional environment and stimulate sustainable economic growth.

Investigating the Impact of Information Distortions on the Resilience of Land-sea Transport Chains Under Business-environment Instability Conditions

Possessing reliable information is the basis for making accurate decisions when planning land-sea transport chains. Modern transport chains create increasingly complicated networks, which affect the decisions made when planning these chains. It should be noted, however, that information distortions may arise at individual stages of the transport process within complex transport chains. The article aims to examine the sources of hazards and risks occurring in land-sea transport chains, to determine the information distortion indicators that may be processed by transport and logistics industry enterprises under conditions of business environment instability, as well as to determine the levels of these chains' resilience to possible information distortions. The article presents the selected types of managerial decision errors. An approach to assessing the impact of distorted information on the decision-making process has been proposed. Information distortion indicators processed by transport and logistics industry enterprises in conditions of business-environment instability were also identified. An attempt was made to determine the possible levels of resilience of these chains to the symptoms of business-environment instability. It was found that, depending on the degree of distortion of the information used by the manager, their decision may be erroneous to a varying degree, while the degree of managerial decisions' incorrectness can be assessed by the number of decision-making cycles required to make and implement an effective decision.

Сбалансированность интересов участников распределительных отношений в контексте обеспечения региональной бюджетной безопасности

This study aims to clarify the concept of budget resilience and substantiate an approach for selecting indicators of regional budget resilience. A content analysis of scientific sources in the field of budget resilience was conducted, and current approaches to defining the concept of budget resilience were classified. The author’s interpretation of the concept is presented, emphasizing the need to select indicators that assess regional budget resilience by considering the interests of public funding recipients. Within this framework, groups of recipients—regional authorities, economic entities, and the population—are identified, and their interests are determined. A system of indicators is proposed to ensure budget resilience in the region, reflecting the level of interest satisfaction among these groups. A comparative analysis of the balance of recipients’ interests based on the results of budget policy and the budget process in the Russian Arctic regions was carried out, and trends in their economic interactions under conditions of global instability were analyzed. The study found vulnerabilities in the budget resilience system, manifested in the infringement of recipients’ interests. Changes in financial market conditions and resource prices led to a decrease in financial results for companies and a reduction in regional output redistributed through budgets, resulting in welfare loss for the regions and their populations. To address the situation, it is necessary to intensify investment activities and business development in the regions and optimize the fiscal regulation system, which will ultimately contribute to the growth of budget and household incomes. Changes in these indicators should be monitored not only in national currency but also in dollar terms to assess the recipients’ financial well-being on an international scale. Future research will focus on selecting specific indicators and their threshold values for assessing budget resilience in the Russian Arctic regions.

Bifurcation Analysis and Spatiotemporal Dynamics in a Diffusive Predator–Prey System Incorporating a Holling Type II Functional Response

This study aims to investigate a diffusive predator–prey system incorporating additional food for predators, prey refuge, fear effect, and its carry-over effects. For the temporal model, the well-posedness and persistence of the system have been discussed. We investigated the existence and the stability behavior of the various equilibria. Furthermore, we explored the bifurcations of codimension-1 including transcritical, saddle-node, and Hopf, concerning the crucial parameters. The system also presents codimension-2 bifurcations such as Bogdanov–Takens and cusp bifurcation along with the global homoclinic bifurcation. We observed the bubbling phenomena, which illustrate the fluctuations in the amplitudes of the periodic oscillations. For the spatiotemporal system, we established the non-negativity and boundedness of the solutions. We derived the conditions for the diffusion-driven instabilities in a confined region with Neumann boundary conditions. Extensive numerical simulations have been conducted to depict the various stationary patterns in Turing space. It is observed that incorporating cross-diffusion divides the bi-parametric plane into various sub-regions and dynamic patterns are analyzed in these different regions. The intricate spatiotemporal dynamics exhibited by prey–predator interactions are crucial for unraveling the intricacies within ecological systems.

Mathematical modeling methods in assessing the prospects of export development in the Republic of Tatarstan of the Russian Federation

In the conditions of instability of the Russian economy, Russian regions have faced the problem of finding new directions of foreign economic development. Mathematical modeling methods, considering the distance between partner regions and their economies volumes, can be effective tools for solving the problem. The article touches upon the modeling foreign trade relations issues in the Republic of Tatarstan on the gravity models’ basis. The purpose of the study is to identify potential trade partners and assess the prospects for the export relations development in the Republic of Tatarstan. The structure, dynamics, and main directions of exports of the constituent entity have been analyzed. Potential trade partners of the Republic of Tatarstan among the Commonwealth of Independent States countries have been identified using the classical gravity model based on assessing the internal regional product and the distance among the regions. The prospects of foreign trade relations with Belarus and the Republic of Uzbekistan have been assessed. Based on J. Tinbergen’s gravity model models of interaction among the regions have been built and forecast values of export volumes for the short term calculated. It was revealed that the Republic of Azerbaijan can become a potential partner for the Republic of Tatarstan. The analysis of the forecast data on the domestic regional product of the Republic of Tatarstan and the gross domestic product of Azerbaijan in 2023 suggests that the exports volume between these entities is expectedly high.