The global stability for a delayed HBV infection model with CTL immune response is investigated. We show that the global dynamics is determined by two sharp thresholds, basic reproduction number <0 and CTL immune-response reproduction number <1. When <0 ≤ 1, the infection-free equilibrium is globally asymptotically stable, which means that the viruses are cleared and immune is not active; when ...

A construction of a globally asymptotically stable time-invariant system which can be destabilized by some integrable perturbation is given. Besides its intrinsic interest, this serves to provide counterexamples to an open question regarding Lyapunov functions.

Necessary and sufficient conditions are obtained for the existence of a globally asymptotically stable equilibrium of a class of delay differential equations modeling the action of a neuron with dynamical threshold effects.

A diffusive Holling–Tanner predator–prey model with no-flux boundary condition is considered, and it is proved that the unique constant equilibrium is globally asymptotically stable under a new simpler parameter condition. © 2011 Elsevier Ltd. All rights reserved.

Necessary and sufficient conditions are obtained for the existence of a globally asymptotically stable equilibrium of a class of delay differential systems modelling the action of two neurons with dynamical threshold effects.

We give an explicit example of a two-dimensional polynomial vector field of degree seven that has rational coefficients, is globally asymptotically stable, but does not admit an analytic Lyapunov function even locally.

In this note we prove that the positive solutions of some classes of rational difference equations are globally asymptotically stable. Using a Berg’s result, we also find asymptotics of some solutions of these equations.  2005 Elsevier Inc. All rights reserved.

We propose a class of delay difference equation with piecewise constant nonlinearity. The convergence of solutions and the existence of globally asymptotically stable periodic solutions are investigated for such a class of difference equation.

A complete stability analysis is performed on a planar discrete-time system of the form ( +1) = sat( ( )), where is a Schur stable matrix and sat is the saturation function. Necessary and sufficient conditions for the system to be globally asymptotically stable are given. In the process of establishing these conditions, the behaviors of the trajectories are examined in detail.