scholarly journals Dynamic Model of Growing File-Sharing P2P Network

2019 ◽  
Vol 26 (3) ◽  
pp. 351-359
Author(s):  
Alexandra I. Kononova ◽  
Larisa G. Gagarina
Keyword(s):  
Differential Equations ◽  
Dynamic Model ◽  
Information Exchange ◽  
Equilibrium Points ◽  
Phase Portraits ◽  
System Of Differential Equations ◽  
First Approximation ◽  
The Stability ◽  
General Provision ◽  
Exchange Network

In this work, the model of development of the P2P file exchange network organized by a torrent tracker is considered. The model is constructed on the basis of ordinary differential equations. The phase variables describing a status of a torrent tracker and the network organized by it (in first approximation is the number of the users of the tracker who are actively participate in information exchange, and the number of active torrents) are defined, the factors influencing the change of users number and the number of torrents are analyzed. On the basis of the analysis the system of differential equations, in first approximation describing evolution of the file exchange network organized by the torrent tracker — a hard dynamic model of evolution of the torrent tracker is written. Equilibrium points of hard model of evolution of the tracker are investigated, their possible quantity and type is described. All configurations of the general provision, possible in a hard model of evolution of the torrent tracker are described. The phase portrait of the hard model is represented. On the basis of the analysis of the hard model the system of differential equations describing evolution of a file exchange network with accounting of dependence of new users inflow intensity on a total quantity of potential audience of the torrent tracker, and also dependences of speed of torrents extinction on the number of users falling on one torrent — a soft dynamic model of evolution of a torrent tracker is written. Equilibrium points of a soft model of tracker evolution are investigated, their possible quantity and type is described. All configurations of the general provision, possible in a soft model of evolution of the torrent tracker are described. Phase portraits of each configuration are represented. The ratio of parameters necessary for the stability of the tracker a stable status is received. The influence of different administrative measures on a stock of the tracker stability in whole is analyzed. The need of support of torrents by administration at highly specialized torrent trackers with small potential audience is shown.

scholarly journals Dynamic Model of Single Torrent with File-Sharing P2P Network

2018 ◽  
Vol 25 (4) ◽  
pp. 421-434
Author(s):  
Alexandra I. Kononova
Keyword(s):  
Differential Equations ◽  
Dynamic Model ◽  
Equilibrium Points ◽  
File Sharing ◽  
P2p Network ◽  
Phase Portraits ◽  
Model Parameters ◽  
Accounting System ◽  
First Approximation ◽  
Over Time

In this work, a model of distribution of the file in P2P file-sharing network constructed on the basis of ordinary differential equations is considered. The phase variables which describe a condition of distribution of the file (as a first approximation is the number of users – seeder and leecher on distribution) are defined, the factors which influence the file distribution and the change of the number of users participating in exchange are analysed. On the basis of the analysis the system of the differential equations describing distribution evolution – dynamic model of evolution of distribution is written down. The life cycle of distribution in file-sharing network consisting of four stages – distribution creation, a fast gain leechers, stabilization and (for distributions of the files losing over time relevance) fading is considered. To each stage there corresponds the ratio of model parameters, and parameters change over time. The process of measuring the condition of real distributions is described. An example of the trajectory corresponding to the evolution of real distribution at a large torrent tracker is shown. Further, the distribution stabilization stage which is characterized by constants as a first approximation parameters is considered. Equilibrium points of the dynamic model of distribution evolution are investigated, their possible quantity and type are described. All configurations of the general position, possible in the model of distribution evolution in a file-sharing P2P network are described. Phase portraits of each configuration are represented. The influence of various administrative measures on a stock of distribution stability is analysed. Ambiguity of the influence of a rating accounting system on the stability of distributions is shown. The positive influence of a system of timebonus, feedback and absorption of distributions is also shown.

scholarly journals A Four-Zone Model and Nonlinear Dynamic Analysis of Solution Multiplicity of Buoyancy Ventilation in Underground Building

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-24
Author(s):  
Yuxing Wang ◽  
Chunyu Wei
Keyword(s):  
Differential Equations ◽  
Equilibrium Point ◽  
Equilibrium Points ◽  
Underground Structure ◽  
Unstable Equilibrium ◽  
Phase Portraits ◽  
Zone Model ◽  
Unstable Equilibrium Point ◽  
Index 2 ◽  
The Stability

The solution multiplicity of natural ventilation in buildings is very important to personnel safety and ventilation design. In this paper, a four-zone model of buoyancy ventilation in typical underground building is proposed. The underground structure is divided to four zones, a differential equation is established in each zone, and therefore, there are four differential equations in the underground structure. By solving and analyzing the equilibrium points and characteristic roots of the differential equations, we analyze the stability of three scenarios and obtain the criterions to determine the stability and existence of solutions for two scenarios. According to these criterions, the multiple steady states of buoyancy ventilation in any four-zone underground buildings for different stack height ratios and the strength ratios of the heat sources can be obtained. These criteria can be used to design buoyancy ventilation or natural exhaust ventilation systems in underground buildings. Compared with the two-zone model in (Liu et al. 2020), the results of the proposed four-zone model are more consistent with CFD results in (Liu et al. 2018). In addition, the results of proposed four-zone model are more specific and more detailed in the unstable equilibrium point interval. We find that the unstable equilibrium point interval is divided into two different subintervals corresponding to the saddle point of index 2 and the saddle focal equilibrium point of index 2, respectively. Finally, the phase portraits and vector field diagrams for the two scenarios are given.

scholarly journals A Dynamic Model of a Belt Driven Electromechanical XY Plotter Cutter

2012 ◽  
Author(s):  
Joseph V. Prisco ◽  
Philip A. Voglewede
Keyword(s):  
Differential Equations ◽  
Dynamic Model ◽  
Motion Control ◽  
Development Time ◽  
Arts And Crafts ◽  
Performance Parameters ◽  
System Of Differential Equations ◽  
Electromechanical Model ◽  
Governing System

Currently, models for XY plotter cutters specific to industrial and arts and crafts applications are not publicly available. This paper mathematically models the XY motion control for a commercial plotter cutter. In this particular application, the Y motion is controlled by media feed and the X motion is controlled by a gantry arm. A dynamic, electromechanical model consisting of a governing system of differential equations for the gantry arm is developed and simulated using Matlab. Once the model is developed, it will be used to decrease development time and optimize performance parameters.

scholarly journals Dynamics Analysis and Control of a Five-Term Fractional-Order System

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Li-xin Yang ◽  
Xiao-jun Liu
Keyword(s):  
Fractional Order ◽  
Equilibrium Points ◽  
Fractional Order System ◽  
Phase Portraits ◽  
Order System ◽  
Bifurcation Diagrams ◽  
Compound Structure ◽  
Dynamical Properties ◽  
The Stability ◽  
And Control

This paper proposes a new fractional-order chaotic system with five terms. Firstly, basic dynamical properties of the fractional-order system are investigated in terms of the stability of equilibrium points, Jacobian matrices theoretically. Furthermore, rich dynamics with interesting characteristics are demonstrated by phase portraits, bifurcation diagrams numerically. Besides, the control problem of the new fractional-order system is discussed via numerical simulations. Our results demonstrate that the new fractional-order system has compound structure.

DYNAMICS OF NUMERICAL METHODS FOR COSYMMETRIC ORDINARY DIFFERENTIAL EQUATIONS

2001 ◽  
Vol 11 (09) ◽  
pp. 2339-2357 ◽  
Author(s):  
V. N. GOVORUKHIN ◽  
V. G. TSYBULIN ◽  
B. KARASÖZEN
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Equilibrium Points ◽  
Two Dimensions ◽  
Model Systems ◽  
Continuous Family ◽  
First Order ◽  
Spurious Solutions ◽  
Overall Performance ◽  
The Stability

The dynamics of numerical approximation of cosymmetric ordinary differential equations with a continuous family of equilibria is investigated. Nonconservative and Hamiltonian model systems in two dimensions are considered and these systems are integrated with several first-order Runge–Kutta methods. The preservation of symmetry and cosymmetry, the stability of equilibrium points, spurious solutions and transition to chaos are investigated by presenting analytical and numerical results. The overall performance of the methods for different parameters is discussed.

scholarly journals Nonlinear Dynamic Analysis of Solution Multiplicity of Buoyancy Ventilation in Two Vertically Connected Open Cavities with Unequal Heights

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Yuxing Wang ◽  
Chunyu Wei
Keyword(s):  
Natural Ventilation ◽  
Equilibrium Points ◽  
Nonlinear Dynamic Analysis ◽  
Phase Portraits ◽  
Stable States ◽  
Characteristic Roots ◽  
Open Cavities ◽  
Personnel Safety ◽  
The Stability ◽  
Upper Room

Solution multiplicity of natural ventilation in buildings is of much importance for personnel safety and ventilation design. In this paper, a new mathematical model of buoyancy pressure ventilation for two vertically connected open cavities is presented. Compared with the previous published papers studying two vertically connected open cavities with equal heights and hot source E2 < 0 in the upper room, we study two vertically connected open cavities with unequal heights and hot source E2 < 0 or E2 > 0 in the upper room. By solving and analyzing the equilibrium points and characteristic roots of the differential equations, we analyze the stability of two systems with upward flow pattern and downward pattern and obtain the criteria to determine the stability and existence of solutions for two scenarios. According to these criteria, the multiple steady states of buoyancy ventilation in two vertically connected open cavities with unequal heights and variable strength of hot sources can be obtained. These criteria can be used to design buoyancy ventilation or natural exhaust ventilation systems in two vertically connected open cavities. Compared with two stable states of buoyancy ventilation existing in two vertically connected open cavities with equal heights in the previously published papers, we find that more stable states and unstable states of buoyancy ventilation exist in two vertically connected open cavities with unequal heights in our paper. Finally, bifurcation diagrams and the phase portraits for the two scenarios are given.

The Model of the Integrated Control of Plant Pests with Natural Enemy

2013 ◽  
Vol 864-867 ◽  
pp. 2522-2527
Author(s):  
Xu Ying Lv ◽  
Tian Wen Yao ◽  
Ding Jiang Wang
Keyword(s):  
Biological Control ◽  
Natural Enemy ◽  
Integrated Control ◽  
Equilibrium Points ◽  
Sufficient Conditions ◽  
Plant Pests ◽  
First Approximation ◽  
Plant Pest ◽  
The Stability ◽  
Hurwitz Theorem

This paper mainly indicates the pest-control problem by using the biological control and the pesticide control. Firstly, it analyzed the continuous changing population of the three species-plants, plant pest and natural enemy-and the pesticides’ effects to establish a three-species model of the pests’ integrated control. Secondly, the pest equilibrium points with the natural enemy and that without natural enemy were obtained. We discussed the stability of the equilibrium points by the Hurwitz theorem and the first approximation method of stability and got the sufficient conditions for asymptotic stability. Finally, numerical simulations were performed by Matlab to analyze and verify the integrated control of plant pests in the situations with some natural enemies and without enemy. Moreover, the effects of spraying pesticides which have different killing rates on enemy and plant pest were analyzed.

scholarly journals Qualitative Analysis of Class of Fractional-Order Chaotic System via Bifurcation and Lyapunov Exponents Notions

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Ndolane Sene
Keyword(s):  
Lyapunov Exponents ◽  
Fractional Order ◽  
Chaotic System ◽  
Numerical Scheme ◽  
Initial Conditions ◽  
Equilibrium Points ◽  
Phase Portraits ◽  
Fractional Chaotic System ◽  
The Stability ◽  
Predictor Corrector

This paper presents a modified chaotic system under the fractional operator with singularity. The aim of the present subject will be to focus on the influence of the new model’s parameters and its fractional order using the bifurcation diagrams and the Lyapunov exponents. The new fractional model will generate chaotic behaviors. The Lyapunov exponents’ theories in fractional context will be used for the characterization of the chaotic behaviors. In a fractional context, the phase portraits will be obtained with a predictor-corrector numerical scheme method. The details of the numerical scheme will be presented in this paper. The numerical scheme will be used to analyze all the properties addressed in this present paper. The Matignon criterion will also play a fundamental role in the local stability of the presented model’s equilibrium points. We will find a threshold under which the stability will be removed and the chaotic and hyperchaotic behaviors will be generated. An adaptative control will be proposed to correct the instability of the equilibrium points of the model. Sensitive to the initial conditions, we will analyze the influence of the initial conditions on our fractional chaotic system. The coexisting attractors will also be provided for illustrations of the influence of the initial conditions.

scholarly journals An Efficient Approach for Solving Fractional Dynamics of a Predator-Prey System

2019 ◽  
Vol 13 (11) ◽  
pp. 116
Author(s):  
Hegagi Mohamed Ali ◽  
Ismail Gad Ameen
Keyword(s):  
Differential Equations ◽  
Numerical Solutions ◽  
Equilibrium Points ◽  
Nonlinear Partial Differential Equations ◽  
Fractional Dynamics ◽  
Predator Prey ◽  
Analytical Technique ◽  
Biological Population ◽  
Fractional Differential ◽  
The Stability

In this work, we execute a generally new analytical technique, the modified generalized Mittag-Leffler function method (MGMLFM) for solving nonlinear partial differential equations containing fractional derivative emerging in predator-prey biological population dynamics system. This dynamics system are given by a set of fractional differential equations in the Caputo sense. A new solution is constructed in a power series. The stability of equilibrium points is studied. Moreover, numerical solutions for different cases are given and the methodology is displayed. We conducted a comparing between the results obtained by our method with the results obtained by other methods to illustrate the reliability and effectiveness of our main results.

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