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...

The concept of inverse systems for standard and positive linear systems is introduced. Necessary and sufficient conditions for the existence of the positive inverse system for continuous-time and discrete-time linear systems are established. It is shown that: 1) The inverse system of continuous-time linear system is asymptotically stable if and only if the standard system is asymptotically stab...

In this paper, a HTLV-I infection model with CTL response is considered. To account for a series of events in infection process, we incorporate a intracellular time delay in the model. We prove that the global dynamics are determined by two threshold parameters R0 and R1, basic reproduction numbers for viral infection and for CTL response, respectively. If R0 < 1, the infection-free equilibrium...

This paper investigates the global stability of virus dynamics model with BeddingtonDeAngelis infection rate. By constructing Lyapunov functions, the global properties have been analyzed. If the basic reproductive ratio of the virus is less than or equal to one, the uninfected steady state is globally asymptotically stable. If the basic reproductive ratio of the virus is more than one, the infe...