Bifurcation and Stability Analysis in Complex Cross-Diffusion Mathematical Model of Phytoplankton-Fish Dynamics

2019 ◽  
Vol 32 (3) ◽  
pp. 207-228
Author(s):  
Hamidou Ouedraogo sci
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Cross Diffusion ◽  
Complex Cross ◽  
Bifurcation And Stability

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.

On the Analysis of Hopf Bifurcation Associated with a Two-Fold Zero Eigenvalue, Part 2: Nonautonomous System

1999 ◽  
Vol 121 (1) ◽  
pp. 105-109 ◽  
Author(s):  
M. Moh’d ◽  
K. Huseyin
Keyword(s):  
Stability Analysis ◽  
Hopf Bifurcation ◽  
Autonomous System ◽  
Critical Value ◽  
Harmonic Excitation ◽  
Nonautonomous System ◽  
External Excitation ◽  
Zero Eigenvalue ◽  
Bifurcation And Stability

This paper extends the bifurcation and stability analysis of the autonomous system considered in Part 1 to the case of a corresponding nonautonomous system. The effect of an external harmonic excitation on the Hopf bifurcation is studied via a modified Intrinsic Harmonic Balancing technique. It is observed that a shift in the critical value of the parameter occurs due to the external excitation. The analysis is carried out with the aid of MAPLE which is also instrumental in verifying the consistency of the approximations conveniently.

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.

scholarly journals Mathematical Analysis of Influenza A Dynamics in the Emergence of Drug Resistance

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Caroline W. Kanyiri ◽  
Kimathi Mark ◽  
Livingstone Luboobi
Keyword(s):  
Mathematical Model ◽  
Sensitivity Analysis ◽  
Drug Resistance ◽  
Stability Analysis ◽  
Influenza A ◽  
Reproduction Number ◽  
Critical Value ◽  
Backward Bifurcation ◽  
Transmission Dynamics ◽  
High Morbidity

Every year, influenza causes high morbidity and mortality especially among the immunocompromised persons worldwide. The emergence of drug resistance has been a major challenge in curbing the spread of influenza. In this paper, a mathematical model is formulated and used to analyze the transmission dynamics of influenza A virus having incorporated the aspect of drug resistance. The qualitative analysis of the model is given in terms of the control reproduction number,Rc. The model equilibria are computed and stability analysis carried out. The model is found to exhibit backward bifurcation prompting the need to lowerRcto a critical valueRc∗for effective disease control. Sensitivity analysis results reveal that vaccine efficacy is the parameter with the most control over the spread of influenza. Numerical simulations reveal that despite vaccination reducing the reproduction number below unity, influenza still persists in the population. Hence, it is essential, in addition to vaccination, to apply other strategies to curb the spread of influenza.

scholarly journals Stability Analysis of a Mathematical Model for Onchocerciaisis Disease Dynamics

2017 ◽  
Vol 21 (4) ◽  
pp. 663
Author(s):  
DU Bako ◽  
NI Akinwande ◽  
AI Enagi ◽  
FA Kuta ◽  
S Abdulrahman
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Disease Dynamics
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