Global properties of the three-dimensional predator-prey Lotka-Volterra systems.
Global stability of delayed Hopfield neural networks under dynamical thresholds.
Global stability of dynamic systems of high order.
Global stability of sets for impulsive differential-difference equations by Lyapunov's direct method
Global stability of sets for systems with impulses.
Global stability of steady solutions for a model in virus dynamics
We consider a simple model for the immune system in which virus are able to undergo mutations and are in competition with leukocytes. These mutations are related to several other concepts which have been proposed in the literature like those of shape or of virulence – a continuous notion. For a given species, the system admits a globally attractive critical point. We prove that mutations do not affect this picture for small perturbations and under strong structural assumptions. Based on numerical...
Global Stability of Steady Solutions for a Model in Virus Dynamics
We consider a simple model for the immune system in which virus are able to undergo mutations and are in competition with leukocytes. These mutations are related to several other concepts which have been proposed in the literature like those of shape or of virulence – a continuous notion. For a given species, the system admits a globally attractive critical point. We prove that mutations do not affect this picture for small perturbations and under strong structural assumptions. Based on numerical...
Globally convergent differential procedures for solving nonlinear systems of equations
Gradient systems of closed operators
A classical result on the existence of global attractors for gradient systems is extended to the case of a semigroup S(t) lacking strong continuity, but satisfying the weaker property of being a closed map for every fixed t ≥ 0.
Growth conditions for the stability of a class of time-varying perturbed singular systems
In this paper, we investigate the problem of stability of linear time-varying singular systems, which are transferable into a standard canonical form. Sufficient conditions on exponential stability and practical exponential stability of solutions of linear perturbed singular systems are obtained based on generalized Gronwall inequalities and Lyapunov techniques. Moreover, we study the problem of stability and stabilization for some classes of singular systems. Finally, we present a numerical example...