Dynamic Systems - Applications in Economy and in Technology

2021 ◽  
Vol 110 ◽  
pp. 9-14
Author(s):  
Dumitru Bălă
Keyword(s):  
Mathematical Model ◽  
Dynamic Systems ◽  
Function Method ◽  
Stability Study ◽  
Regression Method ◽  
Tourism Activity ◽  
The Stability ◽  
The Mathematical Model ◽  
The Way

In this paper, starting from recent data provided by the National Institute of Statistics, we analyze the tourism activity in Mehedinți County. We apply the regression method and analyze some models. We also compare the economic results with those of previous years. Also, in this paper we study the stability of dynamic systems with applications in economics. The stability study is done using the Leapunov function method. The originality of the paper consists in the way we choose the mathematical model in case of regression and in the way we choose the Leapunov function in case of dynamic systems in which we analyze stability.

The Stability Study of Dynamic Systems Using the Leapunov Function Method

2019 ◽  
Vol 34 ◽  
pp. 123-128
Author(s):  
Dumitru Bălă
Keyword(s):  
Dynamical Systems ◽  
Differential Equations ◽  
Dynamic System ◽  
Dynamic Systems ◽  
Function Method ◽  
Autonomous Systems ◽  
Stability Study ◽  
Systems Of Differential Equations ◽  
Stability Theorems ◽  
The Stability

The paper includes the stability study of some dynamical systems given by systems of differential equations. The paper examines the stability of three dynamic systems using the Leapunov function method. The originality of the paper consists of how we choose the Leapunov function. We apply the stability theorems given by Leapunov for autonomous systems. Stability is an important property of a dynamic system that has applications in the technique.

scholarly journals NECESSITY TO IMPROVE THE MATHEMATICAL MODEL OF FREIGHT CARS TO STUDY CASES OF ITS DERAILMENTS

2020 ◽  
pp. 442-451
Author(s):  
А.V. Batig ◽  
A. Ya. Kuzyshyn
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Computer Experiment ◽  
Rolling Stock ◽  
Software Systems ◽  
Freight Car ◽  
The Stability ◽  
The Many ◽  
The Impact ◽  
The Mathematical Model

One of the most important problems that pose a serious threat to the functioning of railways is the problem of freight cars derailment. However, according to statistics, the number of cases of the derailments of freight cars in trains annually grows. Тo prevent such cases, the necessary preventive measures are developed, and to study the causes of their occurrence, a significant number of mathematical models, programs and software systems created by leading domestic and foreign scientists. Studies of such mathematical models by the authors of this work have led to the conclusion that they are not sufficiently detailed to the extent that it is necessary for analyze the reasons of its derailment. At the same time, an analysis of the causes of the rolling stock derailments on the railways of Ukraine over the past five years showed that in about 20 % of cases they are obvious, and in 7 % of cases they are not obvious and implicitly expressed. The study of such cases of rolling stock derailment during an official investigation by the railway and during forensic railway transport expertises requires the use of an improved mathematical model of a freight car, which would allow a quantitative assessment of the impact of its parameters and rail track on the conditions of railway accidents. Therefore, taking into account the main reasons that caused the occurrence of such railroad accidents over the last five years on the railways of Ukraine, the article selected the main directions for improving the mathematical model of a freight car, allowing to cover all the many factors (explicit and hidden) and identify the most significant ones regarding the circumstances of the derailment rolling stock off the track, established on the basis of a computer experiment. It is proposed in the mathematical model of a freight car to take into account the guiding force, the value of which is one of the main indicators of the stability of the rolling stock. The authors of the article noted that not taking into account the influence of the guiding forces on the dynamics of the freight car can lead to an erroneous determination of the reasons for the rolling stock derailment or even to the impossibility of establishing them.

Walking Stability Analysis of Multi-Legged Crablike Robot over Slope

2013 ◽  
Vol 572 ◽  
pp. 636-639
Author(s):  
Xi Chen ◽  
Gang Wang
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Stability Criterion ◽  
Stability Margin ◽  
Static Stability ◽  
Matlab Simulation ◽  
And Performance ◽  
The Stability ◽  
The Mathematical Model ◽  
The Relationship

This paper deals with the walking stability analysis of a multi-legged crablike robot over slope using normalized energy stability margin (NESM) method in order to develop a common stabilization description method and achieve robust locomotion for the robot over rough terrains. The robot is simplified with its static stability being described by NESM. The mathematical model of static stability margin is built so as to carry out the simulation of walking stability over slope for the crablike robot that walks in double tetrapod gait. As a consequence, the relationship between stability margin and the height of the robots centroid, as well as its inclination relative to the ground is calculated by the stability criterion. The success and performance of the stability criterion proposed is verified through MATLAB simulation and real-world experiments using multi-legged crablike robot.

On A Formulation of the Elastic Stability Equations of Circular Cylindrical Shells Under Variable Internal Pressure

1985 ◽  
Vol 9 (2) ◽  
pp. 64-69
Author(s):  
J.L. Urrutia-Galicia ◽  
A.N. Sherbourne
Keyword(s):  
Mathematical Model ◽  
Internal Pressure ◽  
Cylindrical Shells ◽  
Direct Analysis ◽  
Elastic Stability ◽  
Equilibrium Path ◽  
Circular Cylindrical Shells ◽  
The Stability ◽  
Variable Internal Pressure ◽  
The Mathematical Model

The mathematical model of the stability analysis of circular cylindrical shells under arbitrary internal pressure is presented. The paper consists of a direct analysis of the equilibrium modes in the neighbourhood of the unperturbed principal equilibrium path. The final stability condition results in a completely symmetric differential operator which is then compared with current theories found in the literature.

scholarly journals An Approach for the Global Stability of Mathematical Model of an Infectious Disease

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1778
Author(s):  
Mojtaba Masoumnezhad ◽  
Maziar Rajabi ◽  
Amirahmad Chapnevis ◽  
Aleksei Dorofeev ◽  
Stanford Shateyi ◽  
...  
Keyword(s):  
Infectious Disease ◽  
Mathematical Model ◽  
Global Stability ◽  
Incidence Rates ◽  
Endemic Equilibrium ◽  
Symmetry Properties ◽  
Nonlinear Incidence Rates ◽  
Lyapunov Matrix ◽  
The Stability ◽  
The Mathematical Model

The global stability analysis for the mathematical model of an infectious disease is discussed here. The endemic equilibrium is shown to be globally stable by using a modification of the Volterra–Lyapunov matrix method. The basis of the method is the combination of Lyapunov functions and the Volterra–Lyapunov matrices. By reducing the dimensions of the matrices and under some conditions, we can easily show the global stability of the endemic equilibrium. To prove the stability based on Volterra–Lyapunov matrices, we use matrices with the symmetry properties (symmetric positive definite). The results developed in this paper can be applied in more complex systems with nonlinear incidence rates. Numerical simulations are presented to illustrate the analytical results.

Oblique stability of circularly polarized MHD waves

1990 ◽  
Vol 43 (2) ◽  
pp. 257-268 ◽  
Author(s):  
E. Mjølhus ◽  
T. Hada
Keyword(s):  
Mathematical Model ◽  
Finite Amplitude ◽  
Mhd Waves ◽  
Circularly Polarized ◽  
Right Hand ◽  
Wave Trains ◽  
The Stability ◽  
The Right ◽  
The Mathematical Model ◽  
Dnls Equation

The stability of finite-amplitude weakly dispersive circularly polarized MHD wave trains with respect to oblique modulations is investigated. The mathematical model is a multi-dimensional extension of the DNLS equation. We have found that the right-hand-polarized wave, which is stable with respect to parallel modulations, is unstable with respect to certain oblique modulations for most primary wavenumbers.

Structural Decomposition Approach for the Stability of Uncertain Dynamic Systems

1988 ◽  
Vol 55 (4) ◽  
pp. 992-994 ◽  
Author(s):  
Y. H. Chen ◽  
Chieh Hsu
Keyword(s):  
Dynamic Systems ◽  
A Priori ◽  
Parameter Variation ◽  
Stability Study ◽  
Fast Time ◽  
Time Varying ◽  
Decomposition Approach ◽  
New Approach ◽  
Uncertain Dynamic Systems ◽  
The Stability

The stability property for a class of dynamic systems with uncertain parameter variation is studied. The uncertainty can be fast time-varying and unpredictable. A new approach for stability study is proposed. The only required information on the uncertain variation is its possible bound as well as structure. That is, no a priori knowledge on the realization of the variation is needed.

Performance Simulation and Analysis of the Progressive Distributor of the Oil-Air Lubrication by AMEsim

2013 ◽  
Vol 395-396 ◽  
pp. 1227-1232
Author(s):  
Qi Guo Sun ◽  
A Li Cai ◽  
Hong Bo Lv ◽  
Zheng Hui Zhou
Keyword(s):  
Mathematical Model ◽  
Friction Coefficient ◽  
Viscous Friction ◽  
Simulation Method ◽  
Analytic Method ◽  
Performance Simulation ◽  
Air Lubrication ◽  
Oil Flow ◽  
The Stability ◽  
The Mathematical Model

The mathematical model and the simulation model of the progressive distributor are established using an analytic method and AMEsim, a kind of simulation platform, respectively in this paper. The influences of the progressive structure, the viscous friction coefficient, the flow and pressure of the system and the size of throttle orifice on the performance of the progressive distributor are analyzed by the numerical simulation method. The results show that the fluctuations of the flow and pressure of the system are produced due to the overlapping motion of the three pistons, the oil-flow of the progressive distributor can be stabilized by choosing a reasonable viscous friction coefficient, and motion stability of the pistons of the progressive distributor, and the stability of the flow and pressure for the system are influenced by the size of throttle orifice. These conclusions will provide bases for the design of the oil-air lubricating system and the improvement of the structure of the progressive distributor.

scholarly journals Dynamics in Bank Crisis Model

2015 ◽  
Vol 2015 ◽  
pp. 1-5 ◽  
Author(s):  
Tianshu Jiang ◽  
Mengzhe Zhou ◽  
Bi Shen ◽  
Wendi Xuan ◽  
Sijie Wen ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Complex Networks ◽  
Critical Point ◽  
Dynamic Systems ◽  
Degree Distribution ◽  
Equilibrium Points ◽  
Modified Model ◽  
The Past ◽  
Banking Market ◽  
The Stability

Bank crisis is grabbing more serious attention as several financial turmoils have broken out in the past several decades, which leads to a number of researches in this field. Comparing with researches carried out on basis of degree distribution in complex networks, this paper puts forward a mathematical model constructed upon dynamic systems, for which we mainly focus on the stability of critical point. After the model is constructed to describe the evolution of the banking market system, we devoted ourselves to find out the critical point and analyze its stability. However, to refine the stability of the critical point, we add some impulsive terms in the former model. And we discover that the bank crisis can be controlled according to the analysis of equilibrium points of the modified model, which implies the interference from outside may modify the robustness of the bank network.

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