In this paper, we study the positivity and (uniform) exponential stability of a large class perturbed semigroups. Our approach is essentially based on feedback theory infinite-dimensional linear systems. The obtained results are applied to hyperbolic systems including those with delay at boundary conditions. efficiency our theoretical illustrated by some numerical simulations.

the stochastic reaction diffusion systems may suffer sudden shocks‎, ‎in order to explain this phenomena‎, ‎we use markovian jumps to model stochastic reaction diffusion systems‎. ‎in this paper‎, ‎we are interested in almost sure exponential stability of stochastic reaction diffusion systems with markovian jumps‎. ‎under some reasonable conditions‎, ‎we show that the trivial solution of stocha...

The paper is concerned with nonautonomous generalised Nicholson systems under conditions which imply their permanence: by refining the assumptions for permanence, explicit lower and upper uniform bounds all positive solutions are provided, as well criteria global exponential stability of these systems. In particular, periodic systems, existence a globally exponentially attractive solution deriv...

The stability of magnetic states and the mechanism for magnetic transitions can be analyzed in terms of the shape of the energy surface, which gives the energy as a function of the angles determining the orientation of the magnetic moments. Minima on the energy surface correspond to stable or metastable magnetic states and can represent parallel, antiparallel or, more generally, non-collinear a...

The diagonally-invariant exponential stability (DIES) is introduced as a special type of exponential stability (ES) which incorporates information about the sets invariant with respect to the state-space trajectories. DIES is able to unify, at the conceptual level, issues in stability analysis that have been separately addressed by previous researches Unlike ES, DIES is a norm-dependent propert...