In this paper, an HIV-1 infection model with absorption, saturation infection and an intracellular delay accounting for the time between viral entry into a target cell and the production of new virus particles is inve...In this paper, an HIV-1 infection model with absorption, saturation infection and an intracellular delay accounting for the time between viral entry into a target cell and the production of new virus particles is investigated. By analyzing the characteristic equations, the local stability of an infection-free equilibrium and a chronic-infection equilibrium of the model is established. By using suitable Lyapunov functionals and LaSalle＇s invariance principle, it is proved that if the basic reproduction ratio is less than unity, the infection-free equilibrium is globally asymptotically stable; and if the basic reproduction ratio is greater than unity, sufficient condition is derived for the global stability of the chronic-infection equilibrium.展开更多
This paper discusses the relation between the long-time dynamics of solutions of the two-dimensional （2D） incompressible non-Newtonian fluid system and the 2D Navier-Stokes system. We first show that the solutions o...This paper discusses the relation between the long-time dynamics of solutions of the two-dimensional （2D） incompressible non-Newtonian fluid system and the 2D Navier-Stokes system. We first show that the solutions of the non-Newtonian fluid system converge to the solutions of the Navier-Stokes system in the energy norm. Then we establish that the global attractors {.Aε^H}0〈≤1 of the non-Newtonian fluid system converge to the global attractor .A0H of the Navier-Stokes system as ε → 0. We also construct the minimal limit A^H min of the H global attractors {Aε^H}0〈ε≤ as ≤→ 0 and prove that A^Hmin iS a strictly invariant and connected set.展开更多
In this paper, we consider a simple chemostat model with inhibitory exponential sub- strate uptake and a time delay. A detailed qualitative analysis about existence and boundedness of its solutions and the local asymp...In this paper, we consider a simple chemostat model with inhibitory exponential sub- strate uptake and a time delay. A detailed qualitative analysis about existence and boundedness of its solutions and the local asymptotic stability of its equilibria are car- ried out. Using Lyapunov-LaSalle invariance principle, we show that the washout equi- librium is global asymptotic stability for any time delay. Using the fluctuation lemma, the sufficient condition of the global asymptotic stability of the positive equilibrium E＋ is obtained. Numerical simulations are also performed to illustrate the results.展开更多
文摘In this paper, an HIV-1 infection model with absorption, saturation infection and an intracellular delay accounting for the time between viral entry into a target cell and the production of new virus particles is investigated. By analyzing the characteristic equations, the local stability of an infection-free equilibrium and a chronic-infection equilibrium of the model is established. By using suitable Lyapunov functionals and LaSalle＇s invariance principle, it is proved that if the basic reproduction ratio is less than unity, the infection-free equilibrium is globally asymptotically stable; and if the basic reproduction ratio is greater than unity, sufficient condition is derived for the global stability of the chronic-infection equilibrium.
基金supported by National Natural Science Foundation of China(Grant Nos.10901121,11271290 and 11028102)National Basic Research Program of China(Grant No.2012CB426510)+4 种基金Natural Science Foundation of Zhejiang Province(Grant No.Y6080077)Natural Science Foundation of Wenzhou University(Grant No.2008YYLQ01)Zhejiang Youth Teacher Training ProjectWenzhou 551 Projectthe Fundamental Research Funds for the Central Universities(Grant No.2010ZD037)
文摘This paper discusses the relation between the long-time dynamics of solutions of the two-dimensional （2D） incompressible non-Newtonian fluid system and the 2D Navier-Stokes system. We first show that the solutions of the non-Newtonian fluid system converge to the solutions of the Navier-Stokes system in the energy norm. Then we establish that the global attractors {.Aε^H}0〈≤1 of the non-Newtonian fluid system converge to the global attractor .A0H of the Navier-Stokes system as ε → 0. We also construct the minimal limit A^H min of the H global attractors {Aε^H}0〈ε≤ as ≤→ 0 and prove that A^Hmin iS a strictly invariant and connected set.
文摘In this paper, we consider a simple chemostat model with inhibitory exponential sub- strate uptake and a time delay. A detailed qualitative analysis about existence and boundedness of its solutions and the local asymptotic stability of its equilibria are car- ried out. Using Lyapunov-LaSalle invariance principle, we show that the washout equi- librium is global asymptotic stability for any time delay. Using the fluctuation lemma, the sufficient condition of the global asymptotic stability of the positive equilibrium E＋ is obtained. Numerical simulations are also performed to illustrate the results.
