In this paper, we investigate global dynamics for a system of delay differential equations which describes a virus-immune interaction in vivo. The model has two distributed time delays describing time needed for infection of cell and virus replication. Our model admits three possible equilibria, an uninfected equilibrium and infected equilibrium with or without immune response depending on the ...

A nonautonomous Leslie-Gower type food chain model with time delays is investigated. It is proved the general nonautonomous system is permanent and globally asymptotically stable under some appropriate conditions. Furthermore, if the system is periodic one, some sufficient conditions are established, which guarantee the existence, uniqueness, and global asymptotic stability of a positive period...

In this article, we establish the global asymptotic stability of a disease-free equilibrium and an endemic equilibrium of an SIRS epidemic model with a class of nonlinear incidence rates and distributed delays. By using strict monotonicity of the incidence function and constructing a Lyapunov functional, we obtain sufficient conditions under which the endemic equilibrium is globally asymptotica...

In this paper, we introduce two different models of FAST TCP. One is from the original FAST TCP model, and the other is from the ns-2 implementation of FAST TCP. Interestingly, these two models show significantly different dynamic performance and stability characteristics. That is, while the latter model is always globally exponentially stable, the former model is faster than the latter model a...

In this paper, we investigate global dynamics for a system of delay differential equations which describes a virus-immune interaction in vivo. The model has two distributed time delays describing time needed for infection of cell and virus replication. Our model admits three possible equilibria, an uninfected equilibrium and infected equilibrium with or without immune response depending on the ...

According to biological strategy for pest control, we investigate the dynamic behavior of a pest management SEI model with nonlinear incidence concerning impulsive strategyperiodic releasing infected pests at fixed times. We prove that all solutions of the system are uniformly ultimately bounded and there exists a globally asymptotically attractive pest-eradication periodic solution when the im...

In this lecture we introduce a useful tool to study the robustness against disturbances of nonlinear systems. Our starting point is the observation that, given a globally asymptotically stable equilibrium, a small enough perturbation of the vector field should not change the phase portrait much, and hence should not destroy the stability properties. However, how large can the perturbations be b...

the purpose of this paper is to study the convergence and the almost sure t-stability of the modied sp-type random iterative algorithm in a separable banach spaces. the bochner in-tegrability of andom xed points of this kind of random operators, the convergence and the almost sure t-stability for this kind of generalized asymptotically quasi-nonexpansive random mappings are obtained. our resu...

In this paper, we prove the existence of a random fixed point of by using pointwise asymptotically nonexpansive random operator and the stability resultsof two iterative schemes for random operator.

We use feedback control methods to prove existence of globally asymptotically stable equilibria for nonlinear (density dependent) population dynamics. We focus on populations modelled in discrete size or stage classes so that the model has a natural state space of nonnegative vectors in R. Combining comparison results and small gain techniques, we characterize the situations when there is a pos...