scholarly journals Stability Analysis of a Two-Patch Competition Model with Dispersal Delays

2019 ◽  
Vol 2019 ◽  
pp. 1-6
Author(s):  
Guowei Sun ◽  
Ali Mai
Keyword(s):  
Stability Analysis ◽  
Numerical Simulations ◽  
Competition Model ◽  
Competing Species ◽  
Stability And Instability ◽  
The Stability ◽  
Coexistence Equilibrium

In this paper, we study a Lotka-Volterra competition model with two competing species moving randomly between two identical patches. A constant dispersal delay is incorporated into the dispersal process for each species. We show that the dispersal delays do not affect the stability and instability of all four symmetric equilibria. Numerical simulations are presented to demonstrate the effect of dispersal delays on the stability and instability of the symmetric coexistence equilibrium.

scholarly journals The linear instability of the stratified plane Couette flow

2018 ◽  
Vol 853 ◽  
pp. 205-234 ◽  
Author(s):  
Giulio Facchini ◽  
Benjamin Favier ◽  
Patrice Le Gal ◽  
Meng Wang ◽  
Michael Le Bars
Keyword(s):  
Reynolds Number ◽  
Stability Analysis ◽  
Numerical Simulations ◽  
Couette Flow ◽  
Vertical Direction ◽  
Stability Diagram ◽  
Linear Instability ◽  
Plane Couette Flow ◽  
Horizontal Shear ◽  
The Stability

We present the stability analysis of a plane Couette flow which is stably stratified in the vertical direction orthogonal to the horizontal shear. Interest in such a flow comes from geophysical and astrophysical applications where background shear and vertical stable stratification commonly coexist. We perform the linear stability analysis of the flow in a domain which is periodic in the streamwise and vertical directions and confined in the cross-stream direction. The stability diagram is constructed as a function of the Reynolds number $Re$ and the Froude number $Fr$, which compares the importance of shear and stratification. We find that the flow becomes unstable when shear and stratification are of the same order (i.e. $Fr\sim 1$) and above a moderate value of the Reynolds number $Re\gtrsim 700$. The instability results from a wave resonance mechanism already known in the context of channel flows – for instance, unstratified plane Couette flow in the shallow-water approximation. The result is confirmed by fully nonlinear direct numerical simulations and, to the best of our knowledge, constitutes the first evidence of linear instability in a vertically stratified plane Couette flow. We also report the study of a laboratory flow generated by a transparent belt entrained by two vertical cylinders and immersed in a tank filled with salty water, linearly stratified in density. We observe the emergence of a robust spatio-temporal pattern close to the threshold values of $Fr$ and $Re$ indicated by linear analysis, and explore the accessible part of the stability diagram. With the support of numerical simulations we conclude that the observed pattern is a signature of the same instability predicted by the linear theory, although slightly modified due to streamwise confinement.

scholarly journals On the dynamics of a vaccination model with multiple transmission ways

2013 ◽  
Vol 23 (4) ◽  
pp. 761-772 ◽  
Author(s):  
Shu Liao ◽  
Weiming Yang
Keyword(s):  
Stability Analysis ◽  
Disease Control ◽  
Numerical Simulations ◽  
Bifurcation Theory ◽  
Reproduction Number ◽  
Model Predictions ◽  
The Stability ◽  
Disease Free ◽  
Multiple Transmission

Abstract In this paper, we present a vaccination model with multiple transmission ways and derive the control reproduction number. The stability analysis of both the disease-free and endemic equilibria is carried out, and bifurcation theory is applied to explore a variety of dynamics of this model. In addition, we present numerical simulations to verify the model predictions. Mathematical results suggest that vaccination is helpful for disease control by decreasing the control reproduction number below unity.

scholarly journals Stability Analysis of Charged Rotating Black Ring

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1165
Author(s):  
Riasat Ali ◽  
Kazuharu Bamba ◽  
Muhammad Asgher ◽  
Muhammad Fawad Malik ◽  
Syed Asif Ali Shah
Keyword(s):  
Electromagnetic Field ◽  
Field Equation ◽  
Stability Analysis ◽  
Quantum Gravity ◽  
Energy Conservation ◽  
Black Ring ◽  
Back Reaction ◽  
Stability And Instability ◽  
Tunneling Phenomenon ◽  
The Stability

We study the electromagnetic field equation along with the WKB approximation. The boson tunneling phenomenon from charged rotating black ring (CRBR) is analyzed. It is examined that reserve radiation consistent with CRBR can be computed in general by neglecting back reaction and self-gravitational of the radiated boson particle. The calculated temperature depends upon quantum gravity and CRBR geometry. We also examine the corrected tunneling rate/probability of boson particles by assuming charge as well as energy conservation laws and the quantum gravity. Furthermore, we study the graphical behavior of the temperature and check the stability and instability of CRBR.

scholarly journals Stability Analysis for a Fractional HIV Infection Model with Nonlinear Incidence

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Linli Zhang ◽  
Gang Huang ◽  
Anping Liu ◽  
Ruili Fan
Keyword(s):  
Population Dynamics ◽  
Stability Analysis ◽  
Hiv Infection ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Nonnegative Solution ◽  
Infection Model ◽  
Nonlinear Incidence ◽  
Hiv Infection Model ◽  
The Stability

We introduce the fractional-order derivatives into an HIV infection model with nonlinear incidence and show that the established model in this paper possesses nonnegative solution, as desired in any population dynamics. We also deal with the stability of the infection-free equilibrium, the immune-absence equilibrium, and the immune-presence equilibrium. Numerical simulations are carried out to illustrate the results.

scholarly journals Competition between Plasmid-Bearing and Plasmid-Free Organisms in a Chemostat with Pulsed Input and Washout

2009 ◽  
Vol 2009 ◽  
pp. 1-17 ◽  
Author(s):  
Sanling Yuan ◽  
Yu Zhao ◽  
Anfeng Xiao
Keyword(s):  
Periodic Solution ◽  
Stability Analysis ◽  
Numerical Simulations ◽  
Periodic Solutions ◽  
Bifurcation Theory ◽  
Periodic Oscillations ◽  
The Stability ◽  
Invasion Threshold ◽  
Standard Techniques

We consider a model of competition between plasmid-bearing and plasmid-free organisms in the chemostat with pulsed input and washout. We investigate the subsystem with nutrient and plasmid-free organism and study the stability of the boundary periodic solutions, which are the boundary periodic solutions of the system. The stability analysis of the boundary periodic solution yields the invasion threshold of the plasmid-bearing organism. By using the standard techniques of bifurcation theory, we prove that above this threshold there are periodic oscillations in substrate, plasmid-free, and plasmid-bearing organisms. Numerical simulations are carried out to illustrate our results.

scholarly journals Analisis Dinamik Model Transmisi COVID-19 dengan Melibatkan Intervensi Karantina

2021 ◽  
Author(s):  
Resmawan Resmawan ◽  
Agusyarif Rezka Nuha ◽  
Lailany Yahya
Keyword(s):  
Population Dynamics ◽  
Stability Analysis ◽  
Numerical Simulations ◽  
Equilibrium Point ◽  
Equilibrium Points ◽  
Asymptotically Stable ◽  
Human Class ◽  
Existence Of Equilibrium ◽  
The Stability ◽  
Disease Free

This paper discusses the dynamics of COVID-19 transmission by involving quarantine interventions. The model was constructed by involving three classes of infectious causes, namely the exposed human class, asymptotically infected human class, and symptomatic infected human class. Variables were representing quarantine interventions to suppress infection growth were also considered in the model. Furthermore, model analysis is focused on the existence of equilibrium points and numerical simulations to visually showed population dynamics. The constructed model forms the SEAQIR model which has two equilibrium points, namely a disease-free equilibrium point and an endemic equilibrium point. The stability analysis showed that the disease-free equilibrium point was locally asymptotically stable at R0<1 and unstable at R0>1. Numerical simulations showed that increasing interventions in the form of quarantine could contribute to slowing the transmission of COVID-19 so that it is hoped that it can prevent outbreaks in the population.

An extended car-following model considering the low visibility in fog on a highway with slopes

2019 ◽  
Vol 30 (11) ◽  
pp. 1950090
Author(s):  
Jinhua Tan ◽  
Li Gong ◽  
Xuqian Qin
Keyword(s):  
Stability Analysis ◽  
Numerical Simulations ◽  
Traffic Flow ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Neutral Stability ◽  
Car Following ◽  
Low Visibility ◽  
Car Following Model ◽  
The Stability

To depict the effect of low-visibility foggy weather upon traffic flow on a highway with slopes, this paper proposes an extended car-following model taking into consideration the drivers’ misjudgment of the following distance and their active reduction of the velocity. By linear stability analysis, the neutral stability curves are obtained. It is shown that under all the three road conditions: uphill, flat road and downhill, drivers’ misjudgment of the following distance will change the stable regions, while having little effect on the sizes of the stable regions. Correspondingly, drivers’ active reduction of the velocity will increase the stability. The numerical simulations agree well with the analytical results. It indicates that drivers’ misjudgment contributes to a higher velocity. Meanwhile, their active reduction of the velocity helps mitigate the influences of small perturbation. Furthermore, drivers’ misjudgment of the following distance has the greatest effect on downhill and the smallest effect on uphill, so does drivers’ active reduction of the velocity.

Spatial patterns created by cross-diffusion for a three-species food chain model

2014 ◽  
Vol 07 (02) ◽  
pp. 1450013 ◽  
Author(s):  
Canrong Tian ◽  
Zhi Ling ◽  
Zhigui Lin
Keyword(s):  
Stability Analysis ◽  
Numerical Simulations ◽  
Spatial Patterns ◽  
Food Chain ◽  
Turing Instability ◽  
Steady States ◽  
Chain Model ◽  
Cross Diffusion ◽  
The Stability ◽  
Food Chain Model

This paper deals with the stability analysis to a three-species food chain model with cross-diffusion, the results of which show that there is no Turing instability but cross-diffusion makes the model instability possible. We then show that the spatial patterns are spotted patterns by using numerical simulations. In order to understand why the spatial patterns happen, the existence of the nonhomogeneous steady states is investigated. Finally, using the Leray–Schauder theory, we demonstrate that cross-diffusion creates nonhomogeneous stationary patterns.

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