scholarly journals Solutions of a Linearized Mathematical Model for Capillary Formation in Tumor Angiogenesis: An Initial Data Perturbation Approximation

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Serdal Pamuk
Keyword(s):  
Mathematical Model ◽  
Initial Data ◽  
Tumor Angiogenesis ◽  
Cell Movement ◽  
Steady State Solution ◽  
Stability Criteria ◽  
Data Perturbation ◽  
Capillary Formation ◽  
The Stability ◽  
Perturbation Approximation

We present a mathematical model for capillary formation in tumor angiogenesis and solve it by linearizing it using an initial data perturbation method. This method is highly effective to obtain solutions of nonlinear coupled differential equations. We also provide a specific example resulting, that even a few terms of the obtained series solutions are enough to have an idea for the endothelial cell movement in a capillary. MATLAB-generated figures are provided, and the stability criteria are determined for the steady-state solution of the cell equation.

QUALITATIVE ANALYSIS OF A MATHEMATICAL MODEL FOR CAPILLARY FORMATION IN TUMOR ANGIOGENESIS

2003 ◽  
Vol 13 (01) ◽  
pp. 19-33 ◽  
Author(s):  
SERDAL PAMUK
Keyword(s):  
Mathematical Model ◽  
Steady State ◽  
Qualitative Analysis ◽  
Transition Probability ◽  
Steady State Solution ◽  
State Solution ◽  
Transition Probability Density ◽  
Capillary Formation ◽  
Long Time ◽  
The Stability

Qualitative analysis of a mathematical model for capillary formation is presented under assumptions that enzyme and fibronectin concentrations are in quasi-steady state. The aim of this paper is to prove mathematically that the long-time tendency of endothelial cells will be towards the transition probability density function of enzyme and fibronectin. Endothelial cell steady-state solution is obtained and a numerical simulation is provided to show that there is a close agreement between the steady-state solution obtained analytically and the numerically calculated steady-state of the related initial value problem, which provides strong evidence for the stability of this steady-state.

scholarly journals Stabiizing The Steady State Solution of Lasser Fever: Problems and Prospect

2022 ◽  
Vol 05 (01) ◽  
Author(s):  
Innocent C. Eli ◽  
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Control Parameter ◽  
Steady State Solution ◽  
Lassa Fever ◽  
Sexual Contact ◽  
Opposite Sex ◽  
The Stability ◽  
And Control ◽  
Disease Free

The study of mathematical modeling of the stability analysis of Lassa fever was examined. A mathematical model for the spread and control of Lassa fever was formulated and analyzed. The model incorporates a control parameter, the use of condom to control human to human transmission through sexual contact with opposite sex. The disease free and endemic equilibrium states were analyzed.

A MATHEMATICAL MODEL FOR TROPHIC INTERACTIONS IN AN ACARINE PREDATOR-PREY SYSTEM

1995 ◽  
Vol 03 (02) ◽  
pp. 303-312 ◽  
Author(s):  
G. BUFFONI ◽  
G. DI COLA ◽  
J. BAUMGÄRTNER ◽  
V. MAURER
Keyword(s):  
Mathematical Model ◽  
Existence And Uniqueness ◽  
Stability Criteria ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System ◽  
Special Cases ◽  
Behavioral Parameters ◽  
The Stability ◽  
Steady State Solutions

An acarine predator-prey model is introduced and some results concerning the stability of this system are derived. The existence and uniqueness of positive steady state solutions are shown, and stability criteria are estabilished in function of ecological and behavioral parameters. Some special cases include Ivlev and Lotka-Volterra predation. Theoretical and numerical results allow us to assess the feasibility of a biological control of the prey.

Stability and instability of steady-state solutions for a hydrodynamic model of semiconductors

1997 ◽  
Vol 127 (4) ◽  
pp. 781-796 ◽  
Author(s):  
Harumi Hattori
Keyword(s):  
Steady State ◽  
Initial Data ◽  
Positive Constant ◽  
Hydrodynamic Model ◽  
Steady State Solution ◽  
Doping Profile ◽  
Asymptotically Stable ◽  
Stability And Instability ◽  
The Stability ◽  
Steady State Solutions

We discuss the stability and instability of steady-state solutions for a hydrodynamic model of semiconductors. We study the case where the doping profile is close to a positive constant and depends on the special variable x. We shall show that a given steady-state solution is asymptotically stable or unstable, depending on whether or not the density of the initial data satisfies P = 0, where P is defined in (3.12).

TO THE STABILITY OF TANK VEHICLES IN THE BRAKE MODE

2019 ◽  
pp. 27-32
Author(s):  
Denys Popelysh ◽  
Yurii Seluk ◽  
Sergyi Tomchuk
Keyword(s):  
Mathematical Model ◽  
Control Systems ◽  
Distribution Systems ◽  
Traffic Accidents ◽  
Road Traffic ◽  
Center Of Mass ◽  
Dynamic Processes ◽  
Course Stability ◽  
The Stability ◽  
Tank Vehicles

This article discusses the question of the possibility of improving the roll stability of partially filled tank vehicles while braking. We consider the dangers associated with partially filled tank vehicles. We give examples of the severe consequences of road traffic accidents that have occurred with tank vehicles carrying dangerous goods. We conducted an analysis of the dynamic processes of fluid flow in the tank and their influence on the basic parameters of the stability of vehicle. When transporting a partially filled tank due to the comparability of the mass of the empty tank with the mass of the fluid being transported, the dynamic qualities of the vehicle change so that they differ significantly from the dynamic characteristics of other vehicles. Due to large displacements of the center of mass of cargo in the tank there are additional loads that act vehicle and significantly reduce the course stability and the drivability. We consider the dynamics of liquid sloshing in moving containers, and give examples of building a mechanical model of an oscillating fluid in a tank and a mathematical model of a vehicle with a tank. We also considered the method of improving the vehicle’s stability, which is based on the prediction of the moment of action and the nature of the dynamic processes of liquid cargo and the implementation of preventive actions by executive mechanisms. Modern automated control systems (anti-lock brake system, anti-slip control systems, stabilization systems, braking forces distribution systems, floor level systems, etc.) use a certain list of elements for collecting necessary parameters and actuators for their work. This gives the ability to influence the course stability properties without interfering with the design of the vehicle only by making changes to the software of these systems. Keywords: tank vehicle, roll stability, mathematical model, vehicle control systems.

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