The Stability of Nontrivial Positive Steady States for the SKT Model with Large Cross Diffusion

2020 ◽  
Vol 36 (3) ◽  
pp. 657-669
Author(s):  
Qing Li ◽  
Qian Xu
Keyword(s):  
Steady States ◽  
Cross Diffusion ◽  
Positive Steady States ◽  
The Stability

scholarly journals Positive steady states of a ratio-dependent predator-prey system with cross-diffusion

2019 ◽  
Vol 16 (6) ◽  
pp. 6753-6768
Author(s):  
Xiaoling Li ◽  
◽  
Guangping Hu ◽  
Xianpei Li ◽  
Zhaosheng Feng ◽  
...  
Keyword(s):  
Steady States ◽  
Predator Prey ◽  
Cross Diffusion ◽  
Prey System ◽  
Positive Steady States ◽  
Ratio Dependent

Analysis of within-host CHIKV dynamics models with general incidence rate

2018 ◽  
Vol 11 (05) ◽  
pp. 1850062 ◽  
Author(s):  
Ahmed M. Elaiw ◽  
Taofeek O. Alade ◽  
Saud M. Alsulami
Keyword(s):  
Global Stability ◽  
Incidence Rate ◽  
Sufficient Conditions ◽  
Nonlinear Function ◽  
Steady States ◽  
Positive Steady States ◽  
Latently Infected ◽  
The Stability ◽  
Dynamics Models ◽  
Theoretical Results

In this paper we study the stability analysis of two within-host Chikungunya virus (CHIKV) dynamics models. The incidence rate between the CHIKV and the uninfected monocytes is modeled by a general nonlinear function. The second model considers two types of infected monocytes (i) latently infected monocytes which do not generate CHIKV and (ii) actively infected monocytes which produce the CHIKV particles. Sufficient conditions are found which guarantee the global stability of the positive steady states. Using the Lyapunov function, we established the global stability of the steady states of the models. The theoretical results are confirmed by numerical simulations.

Stationary patterns for a Leslie–Gower type three species model with diffusion

2014 ◽  
Vol 07 (06) ◽  
pp. 1450069 ◽  
Author(s):  
Guangping Hu ◽  
Xiaoling Li ◽  
Shiping Lu
Keyword(s):  
Global Stability ◽  
Positive Constant ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Steady States ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Constant Equilibrium ◽  
Positive Steady States ◽  
The Stability

In this paper, a diffusive three species predator–prey model with two Leslie–Gower terms is considered. The stability of the unique positive constant equilibrium for the reaction–diffusion system is obtained. Sufficient conditions are derived for the global stability of the positive constant equilibrium. In particular, we establish the existence and non-existence of non-constant positive steady states of this system. The results indicate that the large diffusivity is helpful for the appearance of the non-constant positive steady states (stationary patterns).

scholarly journals STATIONARY PATTERNS OF A RATIO-DEPENDENT PREDATOR-PREY SYSTEM WITH CROSS-DIFFUSION

2011 ◽  
Vol 16 (3) ◽  
pp. 461-474 ◽  
Author(s):  
Yu-Xia Wang ◽  
Wan-Tong Li ◽  
Hong-Bo Shi
Keyword(s):  
Boundary Condition ◽  
Bounded Domain ◽  
Steady States ◽  
Flux Boundary Condition ◽  
Predator Prey ◽  
Cross Diffusion ◽  
Prey System ◽  
Positive Steady States ◽  
Ratio Dependent ◽  
The Cross

This paper is concerned with a ratio-dependent predator-prey system with diffusion and cross-diffusion in a bounded domain with no flux boundary condition. We establish the existence and non-existence of non-constant positive steady states (patterns). In particular, we show that under certain hypotheses, the cross-diffusion can create stationary patterns even though the corresponding model without cross-diffusion fails.

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