scholarly journals Stability Analysis of a Nonlinear System with Different Growth Functions

2018 ◽  
Vol 37 ◽  
pp. 111-119
Author(s):  
Md Kamrujjaman ◽  
Ashrafi Meher Niger
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Nonlinear System ◽  
Asymptotic Stability ◽  
Carrying Capacity ◽  
Competitive Exclusion ◽  
Logistic Growth ◽  
Limited Growth ◽  
Growth Functions

A competitive mathematical model for the growth of two species is considered in this study. The main goal of the present study is to investigate the roles of two different growth functions: the logistic growth and the food limited growth. We established the main results that determine the asymptotic stability of semi-trivial as well as the coexistence solutions. If higher carrying capacity is embodied for the population following logistic growth then competitive exclusion of a food limited population is imminent and vice versa.GANIT J. Bangladesh Math. Soc.Vol. 37 (2017) 111-119

scholarly journals How the Fractional-order Improve and Extend the Well-known Competitive Exclusion Principle in the Chemostat Model with n Species Competing for a Single Resource?

2019 ◽  
pp. 1-12
Author(s):  
Sayed Sayari ◽  
Miled El Hajji
Keyword(s):  
Mathematical Model ◽  
Fractional Order ◽  
Competitive Exclusion ◽  
Lyapunov Theory ◽  
Exclusion Principle ◽  
Global Dynamics ◽  
Chemostat Model ◽  
Competitive Exclusion Principle ◽  
Growth Functions

In this paper, a fractional-order mathematical model for n species competing, in a chemostat,for a single resource is proposed. The global dynamics was studied using Lyapunov theory, forany set of increasing growth functions. Obtained results generalize and improve the well-knowncompetitive exclusion principle in the chemostat, that one species will eliminate all other species.

Mathematical modeling of the HIV/AIDS epidemic in Cuba

2015 ◽  
Vol 08 (04) ◽  
pp. 1550047 ◽  
Author(s):  
Antonio Mastroberardino ◽  
Yuanji Cheng ◽  
Ahmed Abdelrazec ◽  
Hao Liu
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Stability Analysis ◽  
Nonlinear System ◽  
Transmission Dynamics ◽  
Nonlinear Mathematical Model ◽  
Aids Epidemic ◽  
National Prevention ◽  
Mode Of Transmission ◽  
Hiv Aids

In this paper, a nonlinear mathematical model is presented for the transmission dynamics of HIV/AIDS in Cuba. Due to Cuba's highly successful national prevention program, we assume that the only mode of transmission is through contact with those yet to be diagnosed with HIV. We find the equilibria of the governing nonlinear system, perform a linear stability analysis, and then provide results on global stability.

Early-Warning Model for Tourism Environment Carrying Capacity in Scenic Spots Based on Fuzzy Inference

2012 ◽  
Vol 605-607 ◽  
pp. 2405-2408
Author(s):  
Xiu Ping Yang ◽  
Er Chao Li
Keyword(s):  
Mathematical Model ◽  
Nonlinear System ◽  
Early Warning ◽  
Carrying Capacity ◽  
Early Warning System ◽  
Fuzzy Inference ◽  
Warning System ◽  
Inference System ◽  
Early Warning Model ◽  
Warning Model

Early-warning system of tourism environment carrying capacity (TECC) in scenic spots is a highly complicated nonlinear system. It is very difficult to establish an accuracy mathematical model. Fuzzy inference system adapts to the nonlinear system that doesn’t get an accuracy mathematical model and has uncertain factor. It has strong robustness and adaptability. Index of early-warning system of TECC in scenic spots is established, extracts fuzzy rules based on historical data, and simulates the early-warning system based on fuzzy inference. At last, taking Nandaihe international amusement centre scenic spot as an example proves that the early-warning model designed is feasible and effective.

Kinetic Lyapunov Function for Stability Analysis of Nonlinear Control Systems

1961 ◽  
Vol 83 (1) ◽  
pp. 91-94 ◽  
Author(s):  
S. S. L. Chang
Keyword(s):  
Stability Analysis ◽  
Nonlinear System ◽  
Asymptotic Stability ◽  
Lyapunov Function ◽  
Control Systems ◽  
Local Stability ◽  
Nonlinear Control Systems ◽  
Sufficient Condition ◽  
State Variables ◽  
Derivatives Of

A kinetic Lyapunov function is a Lyapunov function of the first derivatives of the state variables. Its use leads to a sufficient condition for the asymptotic stability in the large of a general nonlinear system without hysteresis. The foregoing sufficient condition is similar to but more stringent than the local stability condition for linearized systems.

scholarly journals Volterra–Lyapunov Stability Analysis of the Solutions of Babesiosis Disease Model

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1272
Author(s):  
Fengsheng Chien ◽  
Stanford Shateyi
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Global Stability ◽  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Disease Model ◽  
Transmission Dynamics ◽  
Global Stability Analysis ◽  
Lyapunov Stability Analysis ◽  
Disease Free

This paper studies the global stability analysis of a mathematical model on Babesiosis transmission dynamics on bovines and ticks populations as proposed by Dang et al. First, the global stability analysis of disease-free equilibrium (DFE) is presented. Furthermore, using the properties of Volterra–Lyapunov matrices, we show that it is possible to prove the global stability of the endemic equilibrium. The property of symmetry in the structure of Volterra–Lyapunov matrices plays an important role in achieving this goal. Furthermore, numerical simulations are used to verify the result presented.

Study on the Calculation Method of Soil-Nailing for High Soil Slope Based on the Logarithmic Spiral Slippery Fracture

2011 ◽  
Vol 261-263 ◽  
pp. 1709-1713
Author(s):  
Meng Yang ◽  
Xiao Min Liu
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Engineering Design ◽  
Calculation Method ◽  
Logarithmic Spiral ◽  
Soil Nailing ◽  
Soil Slope ◽  
Mode Pattern ◽  
Shear Function

This paper introduces a new failure mode pattern of soil slope – the logarithmic spiral slippery fracture. A mathematical model for the logarithmic spiral slippery fracture is established, taking the anti-shear function of the soil-nailing into consideration. The shear of soil-nailing, axial force, and the safety coefficients based on the limiting equilibrium method are derived, leading to an accurate stability analysis of the strengthening of soil slope. A case study shows that the anti-shear function of the soil-nailing can be significant and should not be ignored in engineering design.

scholarly journals Stability of Membrane Elastodynamics with Applications to Cylindrical Aneurysms

2011 ◽  
Vol 2011 ◽  
pp. 1-24 ◽  
Author(s):  
A. Samuelson ◽  
P. Seshaiyer
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Arterial Wall ◽  
Abdominal Aortic Aneurysms ◽  
Medical Problem ◽  
Aortic Aneurysms ◽  
Numerical Techniques ◽  
Abdominal Aortic ◽  
Complex Fluid ◽  
Fluid Solid Interaction

The enlargement and rupture of intracranial and abdominal aortic aneurysms constitutes a major medical problem. It has been suggested that enlargement and rupture are due to mechanical instabilities of the associated complex fluid-solid interaction in the lesions. In this paper, we examine a coupled fluid-structure mathematical model for a cylindrical geometry representing an idealized aneurysm using both analytical and numerical techniques. A stability analysis for this subclass of aneurysms is presented. It is shown that this subclass of aneurysms is dynamically stable both with and without a viscoelastic contribution to the arterial wall.

Analysis and modeling of an inverted pendulum system

2021 ◽  
Author(s):  
Keyword(s):  
Mathematical Model ◽  
Nonlinear System ◽  
Inverted Pendulum ◽  
System Analysis ◽  
Dimensional System ◽  
Two Dimensional ◽  
System Operation ◽  
Pendulum System ◽  
Inverted Pendulum System ◽  
Two Dimensional System

A nonlinear system, which consists of an inverted pendulum mounted on a cart with an electric drive, is considered. A mathematical model is created, its analysis and modeling of the investigated two-dimensional system operation is carried out. Keywords mathematical model; inverted pendulum; system analysis; state space

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